Lectures:  TR 2:00-3:15 pm
Location:  Skiles 255

Instructor:  Edmond Chow
E-mail: 
Office Hours: TBD and after class on Thursdays, and by appointment

TA: Youjie Zhang
TA E-mail:  yzhang3988@gatech.edu
TA Office Hours: TBD and by appointment


Course Description

Introduction to iterative methods for solving linear and nonlinear systems of equations, eigenvalue problems, and optimization.

Prerequisites

Linear Algebra (undergraduate level) and Numerical Linear Algebra (CSE/MATH 6643). The assignments and project will require some programming in any language (at least at the level of CS 1371).

Topics

  • Sparse matrices
  • Basic iterative methods
  • Chebyshev iterative method and matrix polynomials
  • Krylov subspace methods
  • Projection method framework
  • Related ideas for large-scale eigenvalue problems
  • Preconditioning
  • Multigrid methods
  • Methods for nonlinear systems of equations
  • Line search and global convergence
  • Contraction mapping and local convergence theory
  • Nonlinear least squares
  • Related ideas in numerical optimization

Learning Objectives

Students will develop facility with iterative methods for the numerical solution of linear and nonlinear systems, and their analysis. The students will be able to:

  • Given a linear or nonlinear system, choose an appropriate numerical solution method based on the properties of the system
  • Evaulate a method for its convergence and computational cost, including parallel computing aspects
  • Diagnose convergence problems of iterative solution methods
  • Select or design a method or approach for preconditioning the solution of specific problems
  • Use Matlab or other numerical software for solving systems of equations

Grading

30% Assignments (probably 4 in the semester)

15% Individual project: written part due Oct 31; oral part due before Nov 26 (project options will be given in class)

20% Midterm exam in class on Oct 9 (closed book, no computers, with 1 cheat sheet)

30% Final exam (closed book, no computers, with 1 cheat sheet)

5% Class attendance

Audit and Pass/Fail

Please inform the instructor and TA if you are taking the course for audit or pass/fail. For pass/fail, the passing grade is 50% and you must attend class regularly. If you wish to take the course for audit credit, the audit credit is given for a grade of at least 20% and you must attend class regularly.

Recommended Texts

  • Iterative Methods for Sparse Linear Systems, 2nd edition, by Yousef Saad, SIAM, 2003.
  • Numerical Methods for Unconstrained Optimization and Nonlinear Equations, by J. E. Dennis, Jr. and Robert B. Schabel, SIAM, 1996.
  • Matrix Computations, by Gene Golub and C. F. van Loan. Any edition is fine.
You should already have the third book from your course in Numerical Linear Algebra. You can order the first two books from SIAM, here. You can get a 30 percent discount if you are a SIAM member. As a student, you can join SIAM for free, since Georgia Tech is an Academic Member. Check it out here!