Lothar Reichel Technical Reports
PUBLICATIONS SINCE 2001
The files for the publications made available below may differ slightly
from the files for the final versions published in journals and proceedings.
Recent Publications
 S. Noschese and L. Reichel
Communication in multiplex transportation networks
Numer. Algorithms, in press
pdf file
 C. F. Borges and L. Reichel
Computation of Gausstype quadrature rules
Electron. Trans. Numer. Anal., in press
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 S. Noschese and L. Reichel
Edge importance in complex networks
Numer. Algorithms, in press
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 H. Alqahtani, C. F. Borges, D. Lj. Djukic', R. M. Mutavdzic' Djukic', L. Reichel, and
M. M. Spalevic'
Computation of pairs of related Gausstype quadrature rules
Appl. Numer. Math., in press
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 H. Almutairi, D. Lj. Djukic', R. M. Mutavdzic' Djukic', M. S. Pranic',
L. Reichel, and M. M. Spalevic'
Enhanced averaged quadrature rules with application to error estimation
in Analysis, Approximation, Optimization: Computation and
Applications, eds. M. Stanic', M. Albijanic', D. Djurcic', and M. M. Spalevic',
Springer, in press
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 A. Buccini, F. Chen, O. De la Cruz Cabrera, and L. Reichel
Fast alternating fitting methods for trigonometric curves for large data sets
Appl. Numer. Math., in press
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 O. De la Cruz Cabrera, J. Jin, and L. Reichel
Sparse approximation of complex networks
Appl. Numer. Math., in press
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 C. Fenu, L. Reichel, G. Rodriguez, and Y. Zhang
Weighted chained graphs with some applications
Appl. Numer. Math., in press
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IllPosed Problems

A. Buccini, O. De la Cruz Cabrera, C. Koukouvinos, M. Mitrouli, and L. Reichel
Variable selection in saturated and supersaturated designs via l_pl_q minimization
Commun. Statist. Simulation Comput., 52 (2023), pp. 43264347
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 L. Onisk, L. Reichel, and H. Sadok
Numerical considerations of block GMRES methods when applied to
linear discrete illposed problems
J. Comput. Appl. Math., 430 (2023), Art. 115262
pdf file
 A. Buccini and L. Reichel
Limited memory restarted l^pl^q minimization methods using generalized
Krylov subspaces
Adv. Comput. Math., 49 (2023), Art. 26
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 T. Mach, L. Reichel, and M. Van Barel
Adaptive cross approximation for Tikhonov regularization in general form
Numer. Algorithms, 92 (2023), pp. 815830
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 A. Buccini, L. Onisk, and L. Reichel
An Arnoldibased preconditioner for iterated Tikhonov regularization
Numer. Algorithms, 92 (2023), pp. 223245
pdf file
 M. Alkilayh and L. Reichel
Some numerical aspects of ArnoldiTikhonov regularization
Appl. Numer. Math., 185 (2023), pp. 503515
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 A. Alqahtani, R. Ramlau, and L. Reichel
Error estimates for Golub–Kahan bidiagonalization with Tikhonov regularization
for ill–posed operator equations
Inverse Problems, 39 (2023), Art. 025002
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 A. Buccini, M. Donatelli, and L. Reichel
Theoretical and numerical aspects of a nonstationary preconditioned iterative
method for linear discrete illposed problems
J. Comput. Appl. Math., 423 (2023), Art. 114940
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 M. Alotaibi, A. Buccini, and L. Reichel
Krylov subspace split Bregman methods
Appl. Numer. Math., 184 (2023), pp. 371390
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 A. Alqahtani, T. Mach, and L. Reichel
Tikhonov regularization in general form with Chebfun
Proc. Appl. Math. Mech., 22 (2022), Art. e202200041
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 A. Buccini, M. Pragliola, L. Reichel, and F. Sgallari
A comparison of parameter choice rules for l_pl_q minimization
An. Univ. di Ferrara, 68 (2022), pp. 441463
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L. Reichel and U. O. Ugwu
Weighted tensor GolubKahanTikhonovtype methods applied to image processing
using a tproduct
J. Comput. Appl. Math., 415 (2022), Art. 114488
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L. Reichel and U. O. Ugwu
Tensor ArnoldiTikhonov and GMREStype methods for illposed problems with
a tproduct structure
J. Sci. Comput., 90 (2022), Art. 59
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L. Reichel and U. O. Ugwu
The tensor GolubKahanTikhonov method applied to the solution of illposed
problems with a tproduct structure
Numer. Linear Algebra Appl., 29 (2022), e2412
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M. Alotaibi, A. Buccini, and L. Reichel
Restoration of blurred images corrupted by impulse noise via median filters
and l_pl_q minimization
Proc. 21st Intern. Conf. Comput. Sci. Appl. (ICCSA), Cagliari, Italy, 2021,
pp. 112122. Publisher: IEEE, doi: 10.1109/ICCSA54496.2021.00025
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X. Bai, A. Buccini, and L. Reichel
Solution of linear discrete illposed problems by discretized Chebyshev expansion
Proc. 21st Intern. Conf. Comput. Sci. Appl. (ICCSA), Cagliari, Italy, 2021,
pp. 101111. Publisher: IEEE, doi: 10.1109/ICCSA54496.2021.00024
pdf file
 A. Buccini and L. Reichel
Generalized cross validation for l_pl_q minimization
Numer. Algorithms, 88 (2021), pp. 15951616
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 X. Bai, A. Buccini, and L. Reichel
GolubKahan vs. Monte Carlo: A comparison of bidiagonlization and a randomized SVD
method for the solution of linear discrete illposed problems
BIT Numer. Math., 61 (2021), pp. 10931114
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 A. Alqahtani, S. Gazzola, L. Reichel, and G. Rodriguez
On the block Lanczos and block GolubKahan reduction methods applied to discrete illposed problems
Numer. Linear Algebra Appl., 28 (2021), e2376
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 A. Buccini, M. Pasha, and L. Reichel
Linearized Krylov subspace Bregman iteration with nonnegativity constraint
Numer. Algorithms, 87 (2021), pp. 11771200
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L. Reichel and U. O. Ugwu
Tensor Krylov subspace methods with an invertible linear transform product
applied to image processing
Appl. Numer. Math., 166 (2021), pp. 186207
pdf file
 A. Buccini, M. Donatelli, L. Reichel, and W. Zhang
A new nonstationary preconditioned iterative method for linear discrete
illposed problems with application to image deblurring
Numer. Linear Algebra Appl., 28 (2021), e2353
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 A. Buccini, G. Huang, L. Reichel, and F. Yin
On the choice of regularization matrix for an l_2l_q minimization method for
image restoration
Appl. Numer. Math., 164 (2021), pp. 211221
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 X. Bai, G. Huang, X.J. Lei, L. Reichel, and F. Yin
A novel modified TRSVD method for largescale linear discrete illposed problems
Appl. Numer. Math., 164 (2021), pp. 7288
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 L. Dykes, R. Ramlau, L. Reichel, K. Soodhalter, and R. Wagner
Lanczosbased fast blind deconvolution methods
J. Comput. Appl. Math., 382 (2021), Art. 113067
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 A. Buccini, M. Pasha, and L. Reichel
Modulusbased iterative methods for constrained l_pl_q minimization
Inverse Problems, 36 (2020), Art. 084001
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 A. Buccini, O. De la Cruz Cabrera, M. Donatelli, A. Martinelli, and L. Reichel
Largescale regression with nonconvex loss and penalty
Appl. Numer. Math., 157 (2020), pp. 590601
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 F. P. A. Beik, K. Jbilou, M. NajafiKalyani, and L. Reichel
GolubKahan bidiagonalization for illconditioned tensor equations with applications
Numer. Algorithms, 84 (2020), pp. 15351563
pdf file
 L. Reichel, H. Sadok, and W. Zhang
Simple stopping criteria for the LSQR method applied to discrete illposed problems
Numer. Algorithms, 84 (2020), pp. 13811395
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 A. Buccini and L. Reichel
An l_pl_q minimization method with crossvalidation for the restoration of
impulse noise contaminated images
J. Comput. Appl. Math., 375 (2020), Art. 112824
pdf file
 A. Buccini, M. Pasha, and L. Reichel
Generalized singular value decomposition with iterated Tikhonov regularization
J. Comput. Appl. Math., 373 (2020), Art. 112276
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 A. Buccini, Y. Park, and L. Reichel
Comparison of aposteriori parameter choice rules for linear discrete
illposed problems
J. Comput. Appl. Math., 373 (2020), Art. 112138
pdf file
 F. P. A. Beik, M. NajafiKalyani, and L. Reichel
Iterative Tikhonov regularization of tensor equations based on the Arnoldi process and
some of its generalizations
Appl. Numer. Math., 151 (2020), pp. 425447
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 P. Dell'Acqua, M. Donatelli, and L. Reichel
Nonstationary structurepreserving preconditioning for image restoration
in Computational Methods for Inverse Problems in Imaging, eds. M. Donatelli
and S. SerraCapizzano, Springer, Cham, 2019, pp. 5175
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 A. Buccini and L. Reichel
An l_2l_q regularization method for large discrete illposed problems
J. Sci. Comput., 78 (2019), pp. 15261549
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 G. Huang, L. Reichel, and F. Yin
On the choice of subspace for largescale Tikhonov regularization problems in
general form
Numer. Algorithms, 81 (2019), pp. 3355
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 R. Ramlau and L. Reichel
Error estimates for ArnoldiTikhonov regularization for illposed
operator equations
Inverse Problems, 35 (2019), Art. 055002
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 S. Gazzola, S. Noschese, P. Novati, and L. Reichel
Arnoldi decomposition, GMRES, and preconditioning for linear discrete illposed problems
Appl. Numer. Math., 142 (2019), pp. 102121
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 A. H. Bentbib, M. El Guide, K. Jbilou, E. Onunwor, and L. Reichel
Solution methods for linear discrete illposed problems for color image restoration
BIT, 58 (2018), pp. 555578
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 L. Dykes, G. Huang, S. Noschese, and L. Reichel
Regularization matrices for discrete illposed problems in several spacedimensions
Numer. Linear Algebra Appl., 25 (2018), e2163 (16 pages)
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 A. Buccini, Y. Park, and L. Reichel
Numerical aspects of the nonstationary modified linearized Bregman algorithm
Appl. Math. Comput., 337 (2018), pp. 386398
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 Y. Park, L. Reichel, G. Rodriguez, and X. Yu
Parameter determination for Tikhonov regularization problems in general form
J. Comput. Appl. Math., 343 (2018), pp. 1225
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 C. Fenu, L. Reichel, G. Rodriguez, and H. Sadok
GCV for Tikhonov regularization by partial SVD
BIT, 57 (2017), pp. 10191039
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 A. Buccini, M. Donatelli, and L. Reichel
Iterated Tikhonov regularization with a general penalty term
Numer. Linear Algebra Appl., 24 (2017), e2089 (12 pages)
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 L. Dykes, S. Noschese, and L. Reichel
Circulant preconditioners for discrete illposed Toeplitz systems
Numer. Algorithms, 75 (2017), pp. 477490
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 E. Onunwor and L. Reichel
On the computation of a truncated SVD of a large linear discrete illposed problem
Numer. Algorithms, 75 (2017), pp. 359380
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 S. Morigi, L. Reichel, and F. Sgallari
Fractional Tikhonov regularization with a nonlinear penalty term
J. Comput. Appl. Math., 324 (2017), pp. 142154
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 A. H. Bentbib, M. El Guide, K. Jbilou, and L. Reichel
Global GolubKahan bidiagonalization applied to large discrete illposed problems
J. Comput. Appl. Math., 322 (2017), pp. 4656
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 G. Huang, A. Lanza, S. Morigi, L. Reichel, and F. Sgallari
Majorizationminimization generalized Krylov subspace methods for l_pl_q
optimization applied to image restoration
BIT, 57 (2017), pp. 351378
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 Z.Z. Bai, A. Buccini, K. Hayami, L. Reichel, J.F. Yin, and N. Zheng
Modulusbased iterative method for constrained Tikhonov regularization
J. Comput. Appl. Math., 319 (2017), pp. 113
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 C. Fenu, L. Reichel, and G. Rodriguez
GCV for Tikhonov regularization via global GolubKahan decomposition
Numer. Linear Algebra Appl., 23 (2016), pp. 467484
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 S. Gazzola and L. Reichel
A new framework for multiparameter regularization
BIT, 56 (2016), pp. 919949
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 G. Huang, L. Reichel, and F. Yin
On the choice of solution subspace for nonstationary iterated Tikhonov
regularization
Numer. Algorithms, 72 (2016), pp. 10431063
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 G. Huang, L. Reichel, and F. Yin
Projected nonstationary iterated Tikhonov regularization
BIT, 56 (2016), pp. 467487
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S. Noschese and L. Reichel
Some matrix nearness problems suggested by Tikhonov regularization
Linear Algebra Appl., 502 (2016), pp. 366386
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G. Huang, S. Noschese, and L. Reichel
Regularization matrices via matrix nearness problems
Linear Algebra Appl., 502 (2016), pp. 4157
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T. Mach, L. Reichel, M. Van Barel, and R. Vandebril
Adaptive cross approximation for illposed problems
J. Comput. Appl. Math., 303 (2016), pp. 206217
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A. H. Bentbib, M. El Guide, K. Jbilou, and L. Reichel
A global Lanczos method for image restoration
J. Comput. Appl. Math., 300 (2016), pp. 233244
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S. Gazzola, E. Onunwor, L. Reichel, and G. Rodriguez
On the Lanczos and GolubKahan reduction methods applied to discrete illposed
problems
Numer. Linear Algebra Appl., 23 (2016), pp. 187204
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 D. Gerth, E. Klann, R. Ramlau, and L. Reichel
On fractional Tikhonov regularization
J. Inverse IllPosed Probl., 23 (2015), pp. 611625
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 L. Reichel and X. Yu
Tikhonov regularization via flexible Arnoldi reduction
BIT, 55 (2015), pp. 11451168
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 A. Lanza, S. Morigi, L. Reichel, and F. Sgallari
A generalized Krylov subspace method for l_pl_q minimization
SIAM J. Sci. Comput., 37 (2015), pp. S30S50
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 M. E. Hochstenbach, L. Reichel, and X. Yu
A GolubKahantype reduction method for matrix pairs
J. Sci. Comput., 65 (2015), pp. 767789
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 M. E. Hochstenbach, S. Noschese, and L. Reichel
Fractional regularization matrices for linear discrete illposed problems
J. Eng. Math., 93 (2015), pp. 113129
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 A. Bouhamidi, K. Jbilou, L. Reichel, H. Sadok, and Z. Wang
Vector extrapolation applied to truncated singular value decomposition and
truncated iteration
J. Eng. Math., 93 (2015), pp. 99112
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 L. Reichel and X. Yu
Matrix decompositions for Tikhonov regularization
Electron. Trans. Numer. Anal., 43 (2015), pp. 223243
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 T. A. Hearn and L. Reichel
Image denoising via residual kurtosis minimization
Numer. Math. Theor. Meth. Appl., 8 (2015), pp. 403422
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 M. Bellalij, L. Reichel, and H. Sadok
Some properties of range restricted GMRES methods
J. Comput. Appl. Math., 290 (2015), pp. 310318
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 S. Noschese and L. Reichel
Lavrentievtype regularization methods for Hermitian problems
Calcolo, 52 (2015), pp. 187205
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 M. Donatelli, D. Martin, and L. Reichel
Arnoldi methods for image deblurring with antireflective boundary conditions
Appl. Math. Comput., 253 (2015), pp. 135150
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 L. Dykes, S. Noschese, and L. Reichel
Rescaling the GSVD with application to illposed problems
Numer. Algorithms, 68 (2015), pp. 531545
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 M. E. Hochstenbach, L. Reichel, and G. Rodriguez
Regularization parameter determination for discrete illposed problems
J. Comput. Appl. Math., 273 (2015), pp. 132149
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 S. Noschese and L. Reichel
A modified TSVD method for discrete illposed problems
Numer. Linear Algebra Appl., 21 (2014), pp. 813822
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 S. Noschese and L. Reichel
Inverse subspace problems with applications
Numer. Linear Algebra Appl., 21 (2014), pp. 589603
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 S. Morigi, L. Reichel, and F. Sgallari
A general framework for nonlinear regularized Krylovbased image restoration
in CompIMAGE 2014, eds. Y. Zhang and J. M. R. S. Tavares, Lecture Notes in
Computer Science, vol. 8641, Springer, Berlin, 2014, pp. 273279
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 T. A. Hearn and L. Reichel
Application of denoising methods to regularization of illposed problems
Numer. Algorithms, 66 (2014), pp. 761777
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 M. Donatelli and L. Reichel
Square smoothing regularization matrices with accurate boundary conditions
J. Comput. Appl. Math., 272 (2014), pp. 334349
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 L. Dykes, F. Marcellan, and L. Reichel
The structure of iterative methods for
symmetric linear discrete illposed problems
BIT, 54 (2014), pp. 129145
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 T. A. Hearn and L. Reichel
Fast computation of convolution operations via lowrank approximation
Appl. Numer. Math., 75 (2014), pp. 136153
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 K. Morikuni, L. Reichel, and K. Hayami
FGMRES for linear discrete illposed problems
Appl. Numer. Math., 75 (2014), pp. 175187
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 T. A. Hearn and L. Reichel
Extensions of the JustenRamlau blind deconvolution method
Adv. Comput. Math., 39 (2013), pp. 465491
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 D. R. Martin and L. Reichel
Projected Tikhonov regularization of largescale discrete illposed problems
J. Sci. Comput., 56 (2013), pp. 471493
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 L. Dykes and L. Reichel
A family of range restricted iterative methods for linear discrete illposed
problems
Dolomites Research Notes on Approximation, 6 (2013), pp. 2736
postscript file
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 S. Morigi, L. Reichel, and F. Sgallari
A cascadic alternating Krylov subspace image restoration method
in Scale Space and Variational Methods in Computer Vision 2013, eds.
A. Kuijper et al., Lecture Notes in Computer Science, vol 7893,
Springer, Berlin, 2013, pp. 98108
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 L. Dykes and L. Reichel
Simplified GSVD computations for the solution of linear discrete illposed
problems
J. Comput. Appl. Math., 255 (2013), pp. 1527
postscript file
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 L. Reichel and G. Rodriguez
Old and new parameter choice rules for discrete illposed problems
Numer. Algorithms, 63 (2013), pp. 6587
postscript file
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 D. R. Martin and L. Reichel
Minimization of functionals on the solution of a largescale discrete
illposed problem
BIT, 53 (2013), pp. 153173
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 M. K. Khan, S. Morigi, L. Reichel, and F. Sgallari
Iterative methods of RichardsonLucytype for image deblurring
Numer. Math. Theor. Meth. Appl., 6 (2013), pp. 262275
postscript file
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 M. Donatelli, A. Neuman, and L. Reichel
Square regularization matrices for large linear discrete illposed problems
Numer. Linear Algebra Appl., 19 (2012), pp. 896913
postscript file
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 L. Dykes and L. Reichel
On the reduction of Tikhonov minimization problems and the construction of
regularization matrices
Numer. Algorithms, 60 (2012), pp. 683696
postscript file
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 S. Noschese and L. Reichel
Inverse problems for regularization matrices
Numer. Algorithms, 60 (2012), pp. 531544
postscript file
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 L. Reichel, F. Sgallari, and Q. Ye
Tikhonov regularization based on generalized Krylov subspace methods
Appl. Numer. Math., 62 (2012), pp. 12151228
postscript file
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 A. Neuman, L. Reichel, and H. Sadok
Implementations of range restricted iterative methods for linear
discrete illposed problems
Linear Algebra Appl., 436 (2012), pp. 39743990
postscript file
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M. E. Hochstenbach, N. McNinch, and L. Reichel
Discrete illposed leastsquares problems with a solution norm constraint
Linear Algebra Appl., 436 (2012), pp. 38013818
postscript file
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 J. Lampe, L. Reichel, and H. Voss
Largescale Tikhonov regularization via reduction by orthogonal projection
Linear Algebra Appl., 436 (2012), pp. 28452865
postscript file
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M. Fuhry and L. Reichel
A new Tikhonov regularization method
Numer. Algorithms, 59 (2012), pp. 433445
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J. O. Abad, S. Morigi, L. Reichel, and F. Sgallari
Alternating Krylov subspace image restoration methods
J. Comput. Appl. Math., 236 (2012), pp. 20492062
postscript file
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A. Bouhamidi, K. Jbilou, L. Reichel, and H. Sadok
A generalized global Arnoldi method for illposed matrix equations
J. Comput. Appl. Math., 236 (2012), pp. 20782089
postscript file
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 M. E. Hochstenbach and L. Reichel
Combining approximate solutions for linear discrete illposed problems
J. Comput. Appl. Math., 236 (2012), pp. 21792185
pdf file
 E. Klann, R. Ramlau, and L. Reichel
Waveletbased multilevel methods for linear illposed problems
BIT, 51 (2011), pp. 669694
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 M. E. Hochstenbach and L. Reichel
Fractional Tikhonov regularization for linear discrete illposed problems
BIT, 51 (2011), pp. 197215
postscript file
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 A. Bouhamidi, K. Jbilou, L. Reichel, and H. Sadok
An extrapolated TSVD method for linear discrete illposed
problems with Kronecker structure
Linear Algebra Appl., 434 (2011), pp. 16771688
pdf file
 S. Morigi, R. Plemmons, L. Reichel, and F. Sgallari
A hybrid multilevelactive set method for large boxconstrained linear
discrete illposed problems
Calcolo, 48 (2011), pp. 89105
postscript file
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 M. E. Hochstenbach and L. Reichel
An iterative method for Tikhonov regularization with a
general linear regularization operator
J. Integral Equations Appl., 22 (2010), pp. 463480
postscript file
pdf file
 M. E. Hochstenbach and L. Reichel
Subspacerestricted singular value decompositions for linear discrete
illposed problems
J. Comput. Appl. Math., 235 (2010), pp. 10531064
postscript file
pdf file
 S. Morigi, L. Reichel, and F. Sgallari
Cascadic multilevel methods for fast nonsymmetric blur and noiseremoval
Appl. Numer. Math., 60 (2010), pp. 378396
postscript file
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 S. Morigi, L. Reichel, and F. Sgallari
Noisereducing cascadic multilevel methods for linear discrete illposed
problems
Numer. Algorithms, 53 (2010), pp. 122
postscript file
pdf file
 L. Reichel and A. Shyshkov
Cascadic multilevel methods for illposed problems
J. Comput. Appl. Math., 233 (2010), pp. 13141325
postscript file
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 S. Morigi, L. Reichel, and F. Sgallari
An interiorpoint method for large constrained discrete illposed problems
J. Comput. Appl. Math., 233 (2010), pp. 12881297
postscript file
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 S. Morigi, L. Reichel, and F. Sgallari
An edgepreserving multilevel method for deblurring, denoising, and
segmentation
in Scale Space and Variational Methods in Computer Vision, eds. X.C. Tai,
K. Morken, M. Lysaker, and K.A. Lie, Lecture Notes in Computer Science, vol.
5567, Springer, Berlin, 2009, pp. 427438
postscript file
pdf file
 L. Reichel and Q. Ye
Simple square smoothing regularization operators
Electron. Trans. Numer. Anal., 33 (2009), pp. 6383
postscript file
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 L. Reichel, G. Rodriguez, and S. Seatzu
Error estimates for largescale illposed problems
Numer. Algorithms, 51 (2009), pp. 341361
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 K. Jbilou, L. Reichel, and H. Sadok
Vector extrapolation enhanced TSVD for linear discrete illposed problems
Numer. Algorithms, 51 (2009), pp. 195208.
postscript file
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 B. Lewis and L. Reichel
ArnoldiTikhonov regularization methods
J. Comput. Appl. Math., 226 (2009), pp. 92102
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 L. Reichel and A. Shyshkov
A new zerofinder for Tikhonov regularization
BIT, 48 (2008), pp. 627643
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 L. Reichel and H. Sadok
A new Lcurve for illposed problems
J. Comput. Appl. Math., 219 (2008), pp. 493508
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 S. Morigi, L. Reichel, F. Sgallari, and A. Shyshkov
Cascadic multiresolution methods for image deblurring
SIAM J. Imaging Sci., 1 (2008), pp. 5174
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 L. Reichel, H. Sadok, and A. Shyshkov
Greedy Tikhonov regularization for large linear illposed problems
Int. J. Comput. Math., 84 (2007), pp. 11511166
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 S. Morigi, L. Reichel, and F. Sgallari
Orthogonal projection regularization operators
Numer. Algorithms, 44 (2007), pp. 99114
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 S. Morigi, L. Reichel, F. Sgallari, and F. Zama
An iterative method for linear discrete illposed problems with
box constraints
J. Comput. Appl. Math., 198 (2007), pp. 505520
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 J. Baglama and L. Reichel
Decomposition methods for large linear discrete illposed problems
J. Comput. Appl. Math., 198 (2007), pp. 332342
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 S. Morigi, L. Reichel, and F. Sgallari
A truncated projected SVD method for linear discrete illposed problems
Numer. Algorithms, 43 (2006), pp. 197213
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 S. Morigi, L. Reichel, and F. Sgallari
An iterative Lavrentiev regularization method
BIT, 46 (2006), pp. 589606
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 S. Morigi, L. Reichel, F. Sgallari, and F. Zama
Iterative methods for illposed problems and semiconvergent
sequences
J. Comput. Appl. Math., 193 (2006), pp. 157167
postscript file
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 D. Calvetti, L. Reichel, and A. Shuibi
Invertible smoothing preconditioners for linear discrete illposed
problems
Appl. Numer. Math., 54 (2005), pp. 135149
postscript file
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 D. Calvetti, L. Reichel, and A. Shuibi
Tikhonov regularization of large symmetric problems
Numer. Linear Algebra Appl., 12 (2005), pp. 127139
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 D. Calvetti, B. Lewis, L. Reichel, and F. Sgallari
Tikhonov regularization with nonnegativity constraint
Electron. Trans. Numer. Anal., 18 (2004), pp. 153173
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 D. Calvetti, G. Landi, L. Reichel, and F. Sgallari
Nonnegativity and iterative methods for illposed problems
Inverse Problems, 20 (2004), pp. 17471758
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 D. Calvetti and L. Reichel
Tikhonov regularization with a solution constraint
SIAM J. Sci. Comput, 26 (2004), pp. 224239
postscript file
pdf file
 D. Calvetti, L. Reichel, and A. Shuibi
Lcurve and curvature bounds for Tikhonov regularization
Numer. Algorithms, 35 (2004), pp. 301314
postscript file
pdf file
 B. Lewis and L. Reichel
Parallel deconvolution methods for three dimensional image restoration
in Advanced Signal Processing Algorithms, Architecture, and Implementations
XIII, ed. F. T. Luk, Proceedings of the Society of PhotoOptical
Instrumentation Engineers (SPIE), vol. 5205, The International Society for
Optical Engineering, Bellingham, WA, 2003, pp. 291296
postscript file
pdf file
 D. Calvetti and L. Reichel
Tikhonov regularization of large linear problems
BIT, 43 (2003), pp. 263283
postscript file
pdf file
 D. Calvetti, L. Reichel, and A. Shuibi
Enriched Krylov subspace methods for illposed problems
Linear Algebra Appl., 362 (2003), pp. 257273
postscript file
pdf file
 D. Calvetti and L. Reichel
Lanczosbased exponential filtering for discrete illposed problems
Numer. Algorithms, 29 (2002), pp. 4565
postscript file
pdf file
 D. Calvetti, B. Lewis, and L. Reichel
A hybrid GMRES and TVnorm based method for image restoration
in Advanced Signal Processing Algorithms, Architecture, and Implementations
XIII, ed. F. T. Luk, Proceedings of the Society of PhotoOptical
Instrumentation Engineers (SPIE), vol. 4791, The International Society for
Optical Engineering, Bellingham, WA, 2002, pp. 192200
postscript file
pdf file

D. Calvetti, B. Lewis, and L. Reichel
On the regularizing properties of the GMRES method
Numer. Math., 91 (2002), pp. 605625
postscript file
pdf file

D. Calvetti, B. Lewis, and L. Reichel
GMRES, Lcurves, and discrete illposed problems
BIT, 42 (2002), pp. 4465
postscript file
pdf file

D. Calvetti, P. C. Hansen, and L. Reichel
Lcurve curvature bounds via Lanczos bidiagonalization
Electron. Trans. Numer. Anal., 14 (2002), pp. 2035
postscript file
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D. Calvetti, B. Lewis, and L. Reichel
Krylov subspace iterative methods for nonsymmetric discrete illposed
problems in image restoration
in Advanced Signal Processing Algorithms, Architectures, and Implementations XI,
ed. F. T. Luk, Proceedings of the Society of PhotoOptical Instrumentation
Engineers (SPIE), vol. 4474, The International Society for Optical
Engineering, Bellingham, WA, 2001, pp. 224233
postscript file
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D. Calvetti, B. Lewis, and L. Reichel
On the choice of subspace for iterative methods for linear discrete illposed
problems
Int. J. Appl. Math. Comput. Sci., 11 (2001), pp. 10691092
postscript file
pdf file
LargeScale Eigenvalue and Singular Value Problems

A. ElHachimi, K. Jbilou, A. Ratnani, and L. Reichel
A tensor bidiagonalization method for higherorder singular value
decomposition with applications
Numer. Linear Algebra Appl., 31 (2024), Art e2530
pdf file
 A. El Hachimi, K. Jbilou, A. Ratnani, and L. Reichel
Spectral computation with thirdorder tensors using the tproduct
Appl. Numer. Math., 193 (2023), pp. 123
pdf file
 M. Alkilayh, L. Reichel, and Q. Ye
A method for computing a few eigenpairs of large generalized eigenvalue problems
Appl. Numer. Math., 183 (2023), pp. 108117
pdf file
 J. Baglama and L. Reichel
An implicitly restarted block Lanczos bidiagonalization method
using Leja shifts
BIT, 53 (2013), pp. 285310
pdf file
 J. Baglama and L. Reichel
Augmented implicitly restarted Lanczos bidiagonalization methods
SIAM J. Sci. Comput., 27 (2005), pp. 1942
postscript file
pdf file
 J. Baglama, D. Calvetti, and L. Reichel
IRBL: An implicitly restarted block Lanczos method for largescale Hermitian
eigenproblems
SIAM J. Sci. Comput., 24 (2003), pp. 16501677
postscript file
pdf file
Iterative Methods for Linear and Nonlinear Systems of Equations

A. Buccini, P. Diaz de Alba, F. Pes, and L. Reichel
An efficient implementation of the GaussNewton method via
generalized Krylov subspaces
J. Sci. Comput., 97 (2023), Art. 44
pdf file
 J. Ku and L. Reichel
A novel iterative method for discrete Helmholtz decomposition
Appl. Numer. Math., 151 (2020), pp. 161171
pdf file
 J. Ku and L. Reichel
Simple efficient solvers for certain illconditioned systems of linear
equations, including H(div) problems
J. Comput. Appl. Math., 343 (2018), pp. 240249
pdf file
 M. Alkilayh, L. Reichel, and J. Y. Yuan
New zerofinders for trustregion computations
Numer. Algorithms, 76 (2017), pp. 361375
pdf file
 S. Noschese and L. Reichel
A note on superoptimal generalized circulant preconditioners
Appl. Numer. Math., 75 (2014), pp. 188195
pdf file
 J. Baglama, L. Reichel, and D. Richmond
An augmented LSQR method
Numer. Algorithms, 64 (2013), pp. 263293
pdf file
 B. Philippe and L. Reichel
On the generation of Krylov subspace bases
Appl. Numer. Math., 62 (2012), pp. 11711186
postscript file
pdf file
 S. Noschese and L. Reichel
Generalized circulant Strangtype preconditioners
Numer. Linear Algebra Appl., 19 (2012), pp. 317
postscript file
pdf file
 L. Reichel and Q. Ye
A generalized LSQR algorithm
Numer. Linear Algebra Appl., 15 (2008), pp. 643660
postscript file
pdf file
 B. Beckermann and L. Reichel
The Arnoldi process and GMRES for nearly symmetric matrices
SIAM J. Matrix Anal. Appl., 30 (2008), pp. 102120
pdf file
 J. Baglama and L. Reichel
Augmented GMREStype methods
Numer. Linear Algebra Appl., 14 (2007), pp. 337350
pdf file

L. Reichel and Q. Ye
Breakdownfree GMRES for singular systems
SIAM J. Matrix Anal. Appl., 26 (2005), pp. 10011021
postscript file
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D. Calvetti and L. Reichel
Gauss quadrature applied to trust region computations
Numer. Algorithms, 34 (2003), pp. 85102
postscript file
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D. Calvetti and L. Reichel
Pole placement preconditioning
Linear Algebra Appl., 366 (2003), pp. 99120
postscript file
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D. Calvetti, S. Morigi, L. Reichel, and F. Sgallari
An iterative method with error estimators
J. Comput. Appl. Math., 127 (2001), pp. 93119
postscript file
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Integral Equations

L. Fermo, L. Reichel, G. Rodriguez, and M. M. Spalevic'
Averaged Nystrom interpolants for the solution of Fredholm integral
equations of the second kind
Appl. Math. Comput., 467 (2024), Art. 128482
pdf file
Structured Problems in Linear Algebra

S. Noschese and L. Reichel
On the banded Toeplitz structured distance to symmetric positive semidefiniteness
Electron. J. Linear Algebra, 38 (2022), pp. 260273
pdf file
 M. Kuian, L. Reichel, and S. V. Shiyanovskii
Optimally conditioned Vandermondelike matrices
SIAM J. Matrix Anal. Appl., 40 (2019), pp. 13991424
pdf file
 M. Kuian, L. Reichel, and S. V. Shiyanovskii
Fast factorization of rectangular Vandermonde matrices with Chebyshev nodes
Numer. Algorithms, 81 (2019), pp. 547559
pdf file
 S. Noschese and L. Reichel
Eigenvector sensitivity under general and structured perturbations
of tridiagonal Toeplitztype matrices
Numer. Linear Algebra Appl., 26 (2019), e2232 (20 pages)
pdf file
 S. Noschese and L. Reichel
Computing unstructured and structured polynomial pseudospectrum approximations
J. Comput. Appl. Math., 350 (2019), pp. 5768
pdf file
 M. Kuian, L. Reichel, and S. V. Shiyanovskii
Accuracy optimization of combined multiparameter measuring systems with
application to polarized light microscopy
Phys. Rev. E, 97 (2018), 063305 (8 pages)
pdf file
 S. Noschese and L. Reichel
Approximated structured pseudospectra
Numer. Linear Algebra Appl., 24 (2017), e2082 (11 pages)
pdf file
 D. Calvetti, L. Reichel, and H. Xu
A CS decomposition for orthogonal matrices with application to eigenvalue
computation
Linear Algebra Appl., 476 (2015), pp. 197232
pdf file
 C. Jagels and L. Reichel
The structure of matrices in rational Gauss quadrature
Math. Comp., 82 (2013), pp. 20352060
postscript file
pdf file
 S. Noschese, L. Pasquini, and L. Reichel
Tridiagonal Toeplitz matrices: properties and novel applications
Numer. Linear Algebra Appl., 20 (2013), pp. 302326
postscript file
pdf file
 S. Noschese and L. Reichel
The structured distance to normality of Toeplitz matrices with application
to preconditioning
Numer. Linear Algebra Appl., 18 (2011), pp. 429447
postscript file
pdf file
 C. Jagels and L. Reichel
Recursion relations for the extended Krylov subspace method
Linear Algebra Appl., 434 (2011), pp. 17161732
postscript file
pdf file
 S. Noschese and L. Reichel
The structured distance to normality of banded Toeplitz matrices
BIT, 49 (2009), pp. 629640
postscript file
pdf file
 C. Jagels and L. Reichel
The extended Krylov subspace method and orthogonal Laurent polynomials
Linear Algebra Appl., 431 (2009), pp. 441458
postscript file
pdf file
 S. Noschese, L. Pasquini, and L. Reichel
The structured distance to normality of an irreducible real tridiagonal matrix
Electron. Trans. Numer. Anal., 28 (2007), pp. 6577
postscript file
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D. Calvetti, S.M. Kim, and L. Reichel
The restarted QRalgorithm for eigenvalue computation of structured matrices
J. Comput. Appl. Math., 149 (2002), pp. 415422
postscript file
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D. Calvetti, B. Lewis, and L. Reichel
Partial eigenvalue assignment for large linear control systems
Structured Matrices in Mathematics, Computer Science and Engineering I,
ed. V. Olshevsky, Contemporary Mathematics, vol. 280, Amer. Math. Soc.,
Providence, RI, 2001, pp. 241254
postscript file
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D. Calvetti, B. Lewis, and L. Reichel
On the solution of large Sylvesterobserver equations
Numer. Linear Algebra Appl., 8 (2001), pp. 435451
postscript file
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Network Analysis

S. Noschese and L. Reichel
Enhancing multiplex global efficiency
Numer. Algorithms, 96 (2024), pp. 397416
pdf file

S. ElHalouy, S. Noschese, and L. Reichel
A tensor formalism for multilayer network centrality measures using the
Einstein product
Appl. Numer. Math., 200 (2024), pp. 236253
pdf file

S. Noschese and L. Reichel
Network analysis with the aid of the path length matrix
Numer. Algorithms, 95 (2024), pp. 451470
pdf file
 S. ElHalouy, S. Noschese, and L. Reichel
Perron communicability and sensitivity of multilayer networks
Numer. Algorithms, 92 (2023), pp. 597617
pdf file

S. Noschese and L. Reichel
Estimating and increasing the structural robustness of a network
Numer. Linear Algebra Appl., 29 (2022), e2418
pdf file
 A. Concas, C. Fenu, L. Reichel, G. Rodriguez, and Y. Zhang
Chained structure of directed graphs with applications to social and
transportation networks
Appl. Netw. Sci., 7 (2022), Art. 64
pdf file

O. De la Cruz Cabrera, J. Jin, S. Noschese, and L. Reichel
Communication in complex networks
Appl. Numer. Math., 172 (2022), pp. 186205
pdf file
 O. De la Cruz Cabrera, M. Matar, and L. Reichel
Centrality measures for nodeweighted networks via line graphs and the
matrix exponential
Numer. Algorithms, 88 (2021), pp. 583614
pdf file
 A. Concas, L. Reichel, G. Rodriguez, and Y. Zhang
Iterative methods for the computation of the Perron vector of adjacency matrices
Mathematics, 9 (2021), Art. 1522
pdf file
 A. Concas, L. Reichel, G. Rodriguez, and Y. Zhang
Chained graphs and some applications
Appl. Netw. Sci., 6 (2021), Art. 39
pdf file
 O. De la Cruz Cabrera, J. Jin, and L. Reichel
New models for multiclass networks
J. Comput. Appl. Math., 394 (2021), Art. 113567
pdf file

M. Al Mugahwi, O. De la Cruz Cabrera, C. Fenu, L. Reichel, and G. Rodriguez
Block matrix models for dynamic networks
Appl. Math. Comput., 402 (2021), Art. 126121
pdf file
 M. Al Mugahwi, O. De la Cruz Cabrera, S. Noschese, and L. Reichel
Functions and eigenvectors of partially known matrices with applications to
network analysis
Appl. Numer. Math., 159 (2021), pp. 93105
pdf file
 M. Al Mugahwi, O. De la Cruz Cabrera, and L. Reichel
Orthogonal expansion of network functions
Vietnam J. Math., 48 (2020), pp. 941962
pdf file
 A. Concas, S. Noschese, L. Reichel, and G. Rodriguez
A spectral method for bipartizing a network and detecting a large anticommunity
J. Comput. Appl. Math., 373 (2020), Art. 112306
pdf file
 O. De la Cruz Cabrera, M. Matar, and L. Reichel
Edge importance in a network via line graphs and the matrix exponential
Numer. Algorithms, 83 (2020), pp. 807832
pdf file
 O. De la Cruz Cabrera, M. Matar, and L. Reichel
Analysis of directed networks via the matrix exponential
J. Comput. Appl. Math., 355 (2019), pp. 182192
pdf file
 J. Baglama, C. Fenu, L. Reichel, and G. Rodriguez
Analysis of directed networks via partial singular value decomposition and
Gauss quadrature
Linear Algebra Appl., 456 (2014), pp. 93121
pdf file
 C. Fenu, D. Martin, L. Reichel, and G. Rodriguez
Network analysis via partial spectral factorization and Gauss quadrature
SIAM J. Sci. Comput., 35 (2013), pp. A2046A2068
pdf file
Quadrature and Orthogonal Polynomials
 A. Pejcev, L. Reichel, M. M. Spalevic', and S. M. Spalevic'
A new class of quadrature rules for estimating the error in Gauss quadrature
Appl. Numer. Math., 204 (2024), pp. 206221
pdf file

D. Lj. Djukic', R. M. Mutavdzic' Djukic', L. Reichel, and M. M. Spalevic'
Weighted averaged Gaussian quadrature rules for modified Chebyshev measures
Appl. Numer. Math., 200 (2024), pp. 195208
pdf file

H. Almutairi, M. Pranic', and L. Reichel
Error estimates for quadrature rules based on the Arnoldi process
J. Comput. Appl. Math., 442 (2024), Art. 115726
pdf file

D. Lj. Djukic', R. M. Mutavdzic' Djukic', L. Reichel, and M. M. Spalevic'
Decompositions of optimal averaged Gauss quadrature rules
J. Comput. Appl. Math., 438 (2024), Art. 115586
pdf file
 L. Reichel and M. M. Spalevic'
Radau and Lobatto averaged Gaussian quadrature rules
J. Comput. Appl. Math., 437 (2024), Art. 115475
pdf file

D. Lj. Djukic', R. M. Mutavdzic' Djukic', L. Reichel, and M. M. Spalevic'
Internality of averaged Gauss quadrature rules for certain modification
of Jacobi measures
Appl. Comput. Math. (Baku), 22 (2023), pp. 426442
pdf file
 D. Lj. Djukic', R. M. Mutavdzic' Djukic', L. Reichel, and M. M. Spalevic'
Internality of generalized averaged Gauss quadrature rules and truncated
variants for modified Chebyshev measures of the third and fourth kinds
Numer. Algorithms, 92 (2023), pp. 523544
pdf file
 A. Bentbib, M. El Ghomari, K. Jbilou, and L. Reichel
The global GolubKahan method and Gauss quadrature for tensor function
approximation
Numer. Algorithms, 92 (2023), pp. 534
pdf file

J. Alahmadi, M. Pranic', and L. Reichel
Pole allocation for rational Gauss quadrature rules for matrix functionals
defined by a Stieltjes function
Axioms, 12 (2023), Art. 105
pdf file

J. Alahmadi, M. Pranic', and L. Reichel
Rational Gauss quadrature rules for the approximation of matrix functionals
involving Stieltjes functions
Numer. Math., 151 (2022), pp. 443473
pdf file

L. Reichel and M. M. Spalevic'
Averaged Gauss quadrature formulas: Properties and applications
J. Comput. Appl. Math., 410 (2022), Art. 114232
pdf file

A. Bentbib, M. El Ghomari, K. Jbilou, and L. Reichel
The extended symmetric block Lanczos method for matrixvalued Gausstype
quadrature rules
J. Comput. Appl. Math., 407 (2022), Art. 113965
pdf file
 J. Alahmadi, H. Alqahtani, M. S. Pranic', and L. Reichel
GaussLaurenttype quadrature rules for the approximation of functionals of a
nonsymmetric matrix
Numer. Algorithms, 88 (2021), pp. 19371964
pdf file
 D. Lj. Djukic', R. M. Mutavdzic' Djukic', L. Reichel, and
M. M. Spalevic'
Internality of generalized averaged Gauss quadrature rules and truncated variants
for modified Chebyshev measures of the first kind
J. Comput. Appl. Math., 398 (2021), Art. 113696
pdf file
 J. Alahmadi, M. S. Pranic', and L. Reichel
Computation of error bounds via generalized GaussRadau and
GaussLobatto rules
J. Comput. Appl. Math., 396 (2021), Art. 113604
pdf file
 L. Reichel and M. M. Spalevic'
A new representation of generalized averaged Gauss quadrature rules
Appl. Numer. Math., 165 (2021), pp. 614619
pdf file
 A. H. Bentbib, M. El Ghomari, K. Jbilou, and L. Reichel
Shifted extended global Lanczos processes for trace estimation with application
to network analysis
Calcolo, 58 (2021), Art. 4
pdf file
 N. Eshghi, T. Mach, and L. Reichel
New matrix function approximations and quadrature rules based on the Arnoldi
process
J. Comput. Appl. Math., 391 (2021), Art. 113442
pdf file
 C. Jagels, K. Jbilou, and L. Reichel
The extended global Lanczos method, GaussRadau quadrature, and matrix function approximation
J. Comput. Appl. Math., 381 (2021), Art. 113027
pdf file
 L. Reichel, M. M. Spalevic', and J. D. Tomanovic'
Rational averaged Gauss quadrature rules
FILOMAT, 34:2 (2020), pp. 379389
pdf file
 H. Alqahtani and L. Reichel
Generalized block antiGauss quadrature rules
Numer. Math., 143 (2019), pp. 605648
pdf file
 D. Lj. Djukic', L. Reichel, and M. M. Spalevic'
Internality of generalized averaged Gaussian quadrature rules and
truncated variants for measures induced by Chebyshev polynomials
Appl. Numer. Math., 142 (2019), pp. 190205
pdf file
 D. Lj. Djukic', L. Reichel, M. M. Spalevic', and J. D. Tomanovic'
Internality of generalized averaged Gaussian quadrature rules and truncated
variants for modified Chebyshev measures of the second kind
J. Comput. Appl. Math., 345 (2019), pp. 7085
pdf file
 A. H. Bentbib, M. El Ghomari, C. Jagels, K. Jbilou, and L. Reichel
The extended global Lanczos method for matrix function approximation
Electron. Trans. Numer. Anal., 50 (2018), pp. 144163
pdf file
 H. Alqahtani and L. Reichel
Multiple orthogonal polynomials applied to matrix function evaluation
BIT, 58 (2018), pp. 835859
pdf file
 H. Alqahtani and L. Reichel
Simplified antiGauss quadrature rules with applications in linear algebra
Numer. Algorithms, 77 (2018), pp. 577602
pdf file
 N. Eshghi, L. Reichel, and M. M. Spalevic
Enhanced matrix function approximation
Electron. Trans. Numer. Anal., 47 (2017), pp. 197205
pdf file
 C. Jagels, L. Reichel, and T. Tang
Generalized averaged Szego quadrature rules
J. Comput. Appl. Math., 311 (2017), pp. 645654
pdf file
 D. Lj. Djukic', L. Reichel, M. M. Spalevic', and J. D. Tomanovic'
Internality of generalized averaged Gauss rules and their truncations for
BernsteinSzego weights
Electron. Trans. Numer. Anal., 45 (2016), pp. 405419
pdf file
 D. Lj. Djukic', L. Reichel, and M. M. Spalevic'
Truncated generalized averaged Gauss quadrature rules
J. Comput. Appl. Math., 308 (2016), pp. 408418
pdf file
 L. Reichel, G. Rodriguez, and T. Tang
New block quadrature rules for the approximation of matrix functions
Linear Algebra Appl., 502 (2016), pp. 299326
pdf file
 L. Reichel, M. M. Spalevic', and T. Tang
Generalized averaged Gauss quadrature rules for the approximation of
matrix functionals
BIT, 56 (2016), pp. 10451067
pdf file
 C. Jagels and L. Reichel
On the computation of Gauss quadrature rules for measures with a monomial
denominator
J. Comput. Appl. Math., 286 (2015), pp. 102113
pdf file
 M. S. Pranic' and L. Reichel
Generalized antiGauss quadrature rules
J. Comput. Appl. Math., 284 (2015), pp. 235243
pdf file
 M. Bellalij, L. Reichel, G. Rodriguez, and H. Sadok
Bounding matrix functionals via partial global block Lanczos decomposition
Appl. Numer. Math., 94 (2015), pp. 127139
pdf file
 M. S. Pranic' and L. Reichel
Rational Gauss quadrature
SIAM J. Numer. Anal., 52 (2014), pp. 832851
pdf file
 L. Reichel
Polynomials orthogonal on the semicircle
in Walter Gautschi: Selected Works with Commentaries, vol. 2, eds. C. Brezinski and
A. Sameh, Springer, New York, 2014, pp. 1722
pdf file
 C. Fenu, D. Martin, L. Reichel, and G. Rodriguez
Block Gauss and antiGauss quadrature with application to networks
SIAM J. Matrix Anal. Appl., 34 (2013), pp. 16551684
pdf file
 S.M. Kim and L. Reichel
Sensitivity analysis for Szego polynomials
Numer. Math., 113 (2009), pp. 265279
postscript file
pdf file
 B. de la Calle Ysern, G. Lo'pez Lagomasino, and L. Reichel
Stieltjestype polynomials on the unit circle
Math. Comp., 78 (2009), pp. 969997
postscript file
pdf file
 G. Lo'pez Lagomasino, L. Reichel, and L. Wunderlich
Matrices, moments, and rational quadrature
Linear Algebra Appl., 429 (2008), pp. 25402554
postscript file
pdf file
 S.M. Kim and L. Reichel
AntiSzego quadrature rules
Math. Comp., 76 (2007), pp. 795810
postscript file
pdf file
 C. Jagels and L. Reichel
SzegoLobatto quadrature rules
J. Comput. Appl. Math., 200 (2007), pp. 116126
postscript file
pdf file

D. Calvetti, S.M. Kim, and L. Reichel
Quadrature rules based on the Arnoldi process
SIAM J. Matrix Anal., 26 (2005), pp. 765781
postscript file
pdf file

D. Calvetti and L. Reichel
Symmetric GaussLobatto and modified antiGauss rules
BIT, 43 (2003), pp. 541554
postscript file
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Polynomial Computation, Rational Approximation, and Matrix Functions

D. Lj. Djukic', R. M. Mutavdzic' Djukic', L. Reichel, and M. M. Spalevic'
Optimal averaged Pade'type approximants
Electron. Trans. Numer. Math., 59 (2023), pp. 145156
pdf file
 N. Eshghi and L. Reichel
Estimating the error in matrix function approximations
Adv. Comput. Math., 47 (2021), Art. 57
pdf file
 M. Pranic', L. Reichel, G. Rodriguez, Z. Wang, and X. Yu
A rational Arnoldi process with applications
Numer. Linear Algebra Appl., 23 (2016), pp. 10071022
pdf file
 C. Jagels, T. Mach, L. Reichel, and R. Vandebril
Convergence rates for inversefree rational approximation of matrix functions
Linear Algebra Appl., 510 (2016), pp. 291310
pdf file
 M. S. Pranic' and L. Reichel
Recurrence relations for orthogonal rational functions
Numer. Math., 123 (2013), pp. 629642
postscript file
pdf file
 B. Beckermann and L. Reichel
Error estimation and evaluation of matrix functions via the Faber transform
SIAM J. Numer. Anal., 47 (2009), pp. 38493883
pdf file

D. Calvetti and L. Reichel
On the evaluation of polynomial coefficients
Numer. Algorithms, 33 (2003), pp. 153161
postscript file
pdf file

D. Calvetti, L. Reichel, and F. Sgallari
A modified companion matrix method based on Newton polynomials
Fast Algorithms for Structured Matrices: Theory and Applications, ed. V.
Olshevsky, Contemporary Mathematics, vol. 323, Amer. Math. Soc., Providence,
RI, 2003, pp. 179186
postscript file
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G. S. Ammar, D. Calvetti, W. B. Gragg, and L. Reichel
Polynomial zerofinders based on Szego polynomials
J. Comput. Appl. Math., 127 (2001), pp. 116
postscript file
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Bioinformatics
 Z.H. Duan, B. Hughes, L. Reichel, D. M. Perez, and T. Shi
The relationship between protein sequences and their gene ontology functions
BMC Bioinformatics, 7 (Suppl 4) (2006), S11 (11 pages)
html file
Software
 A. Buccini and L. Reichel
Software for limited memory restarted l_pl_q minimization methods
using generalized Krylov subspaces
Electron. Trans. Numer. Anal., 61 (2024), pp. 6691
pdf file
 A. Buccini, L. Onisk, and L. Reichel
Range restricted iterative methods for linear discrete illposed problems
Electron. Trans. Numer. Anal., 58 (2023), pp. 348377
pdf file
 A. Alqahtani, T. Mach, and L. Reichel
Solution of illposed problems with Chebfun
Numer. Algorithms, 92 (2023), pp. 23412364
pdf file
 C. Fenu, L. Reichel, and G. Rodriguez
SoftNet: A package for the analysis of complex networks
Algorithms, 15 (2022), Art. 296
pdf file
 J. Baglama, L. Reichel, and B. W. Lewis
irlba: Fast truncated SVD, PCA and symmetric eigendecomposition for large
dense and sparse matrices
R package version 2.1.2, 2016. Available at https://CRAN.Rproject.org/package=irlba
This is a package for the statistical computing environment R. It is the leading
algorithm for truncated SVD computations. The algorithm has been downloaded more
than one million times.
 A. Neuman, L. Reichel, and H. Sadok
Algorithms for range restricted iterative
methods for linear discrete illposed problems
Numer. Algorithms, 59 (2012), pp. 325331
postscript file
pdf file
 J. Baglama and L. Reichel
Restarted block Lanczos bidiagonalization methods
Numer. Algorithms, 43 (2006), pp. 251272
postscript file
pdf file

J. Baglama, D. Calvetti, and L. Reichel
Algorithm 827: irbleigs: A MATLAB program for computing a few eigenpairs
of a large sparse Hermitian matrix
ACM Trans. Math. Software, 29 (2003), pp. 337348
postscript file
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