**Lectures:** TR 1:30-2:45 pm

**Location:** Clough 423

**Instructor:** Edmond Chow

**E-mail:**

**Office Hours:** By appointment in KACB 1312

**TA:** Jamie Budai

**TA E-mail:** jbudai6@gatech.edu

**TA Office Hours:** Tuesdays 10:55-11:55 and Wednesdays 12:05-1:05 pm, in Skiles 154, and by appointment

**Course Description**

Introduction to the state-of-the-art iterative methods for solving linear and nonlinear systems of equations. This will be a very practical course, involving Matlab programming and a project.

**Prerequisites**

**Topics**

- Sparse matrices and review of direct methods
- Basic iterative methods (splitting methods, Jacobi, Gauss-Seidel, SOR)
- Chebyshev iterative method and matrix polynomials
- Krylov subspace methods (conjugate gradient method, GMRES, etc.)
- Projection method framework
- Methods based on biorthogonalization
- Iterative methods for linear least squares
- Preconditioning
- Multigrid methods
- Domain decomposition
- Nonlinear systems of equations (fixed point methods, Newton, Broyden, Newton-Krylov and other Newton variants for large problems)
- Line search and global convergence
- Contraction mapping and local convergence theory
- Nonlinear least squares (Gauss-Newton, Levenberg-Marquardt)
- Related ideas in 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**

50% Assignments

40% Project (progress reports, in-class presentation, final report)

10% Class participation

**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__, 4th edition, by Gene Golub and C. F. van Loan, Johns Hopkins, 2013.