TIME & PLACE: Mo + We 2:15 - 3:30 pm, MSB 158 or online

TEXTBOOKS:

L. N. Trefethen and D. Bau, Numerical Linear Algebra, SIAM, Philadelphia, 1997.

J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, 3rd ed., Springer, New York, 2002. (Other editions are also fine.)

INSTRUCTOR:

• Lothar Reichel, office 366 MSB, phone: 330-672-9114, e-mail: reichel@math.kent.edu, home page: http://www.math.kent.edu/~reichel
• Office hours: Mo + We 3:30 - 4:30 pm and by appointment.

The beginning of the course focuses on Numerical Linear Algebra, in particular on the computation of eigenvalues and eigenvectors of a matrix, and on iterative methods for the solution of large linear systems of equations. The most powerful solution methods depend implicitly on recursion relations of families of orthogonal polynomials. We discuss these properties in the context of polynomial approximation of a smooth function. Gauss quadrature rules are discussed next. They also depend on orthogonal polynomials. Approximation by piece-wise polynomials (splines), rational functions, and trigonometric polynomials also is considered. The latter computations can conveniently be carried out with the fast Fourier transform method. The course is concluded with a discussion on iterative solution methods for nonlinear (systems) of equations.

The programming languages MATLAB and GNU Octave will be taught. Octave is similar to MATLAB, and available for free. The performance and properties of the numerical methods discussed will be illustrated using MATLAB. All students should get accounts on the Math/CS Network on which MATLAB is available. GNU Octave is a public domain language very similar to MATLAB, and can be used for homework assignments. Instructions on how to install GNU Octave on your PC are available here.

• Computation of eigenvalues and eigenvectors of small and large matrices.
• Iterative methods for the solution of large linear systems of equations.
• Orthogonal polynomials and Gauss quadrature.
• Polynomial interpolation, piecewise polynimial approximation
• Approximation by rational functions.
• Approximation by trigonometric polynomials, the fast Fourier transform (FFT).
• Iterative solution methods for nonlinear scalar and systems of equations.

Homework will be assigned and collected most weeks. There will be a mid-term exam and a final exam. Homework problems can be found here.

Homework and numerical experiments contribute 20%, the midterm 40%, and the final exam 40%.

Numerical Analysis I or a similar course. Contact instructor if you would like to take the course, but do not satisfy the prerequisite.

The official registration deadline for this course is 1/20/19. University policy requires all students to be officially registered in each class they are attending. Students who are not officially registered for a course by the published deadlines should not be attending classes and will not receive credit or a grade for the course. Each student must confirm enrollment by checking his/her class schedule (using Student Tools in FlashLine) prior to the deadline indicated. Registration errors must be corrected prior to the deadline. Last day to withdraw is 3/26/17.

Presenting someone else's work as your own is discussed here. This includes finding the answer of a homework problem in a book, on the internet, or in someone else's assignment, and copying it. Plagiarism, of course, is unacceptable.

University policy requires that students with disabilities be provided reasonable accommodations to ensure their equal access to course content. If you have a documented disability and require accommodations, then please contact the instructor at the beginning of the semester to make arrangements for necessary classroom adjustments. Please note, you must first verify your eligibility for these through Student Accessibility Services (contact 330-672- 3391 or visit www.kent.edu/sas for more information on registration procedures).

USEFUL LINKS:

• MATLAB is the programming language for this class. A 39-page primer on the basics of MATLAB is available in pdf and in postscript.


• Links to online MATLAB tutorials:
  • MATLAB guide
    
  • Gigantic MATLAB tutorial
    


• Software, manuals and glossaries
  • Linear Algebra Glossary
  • The NEOS guide to optimization technology and the NEOS server for solving optimization problems remotely over the internet.
  • Decision Tree for Optimization Software (by H. D. Mittelmann and P. Spellucci).
  • GAMS, Guide to Available Mathematical Software.
  • Netlib, a collection of mathematical software, papers, and databases.
  
  
• The importance of reliable software:
  • Two disasters caused by computer arithmetic errors
  
  
  January 2017