## Fall 2021

### MATH 62263/72263: Numerical Solution of Large Sparse Linear Systems

Many problems in applied mathematics, physics, chemistry, and engineering
give rise to large sparse linear systems of equations. Standard solution
methods for small systems of equations, such as Gaussian elimination and
Cholesky factorization, cannot be used, because these methods require
too much arithmetic work and computer storage to be practical for large
problems. Large linear systems of equations are typically solved by
iterative methods. This course provides up-to-date coverage of iterative
methods for solving large sparse linear systems. The course presents the
theory behind numerous state-of-the-art iterative methods, including the
Conjugate Gradient, Generalized Minimal Residual, Bi-Conjugate Gradient
and Quasi-Minimal Residual methods. Orthogonal and oblique projections are
emphasized, because many of the iterative methods discussed can be understood
in terms of projections. Practical issues, such as storage
schemes for sparse matrices, the discretization of partial differential
equations and parallel implementation, are also addressed. MATLAB
implementations of iterative methods provides valuable hands-on
experience. We will discuss applications of the techniques discussed to
the solution of large systems of equations that arise in data science.