Credits -- 4 (4-0-0)
Term Offered -- Spring
Prerequisite -- M369 or higher and preparedness to do programming in
a standard language
- Text
-- - There are many possible
texts. One of them is: Trefethen, L.N. and Bau, D., Numerical
Linear Algebra, 1997, SIAM.
- Course Objective
-- - To provide our
graduate students with a broad overview on basic topics in Numerical
Linear Algebra. Problem solving is emphasized.
Course Content --
- Factorization Methods for Matrices
(a) Gauss Elimination and LU Factorization
(b) Cholesky Factorization
(c) QR Factorization
(d) Singular Value Decomposition
(e) Underdetermined and Overdetermined Systems
(f) Stability Analysis
- Iterative Methods for Linear Equations
(a) Jacobi, Gauss-Seidel, SOR
(b) Conjugate Gradient Methods
(c) Krylov Subspace Methods
- Eigenvalue Problems
(a) Power Method, Inverse Iteration
(b) QR Algorithm
(c) Jacobi Method
(d) Lanczos Methods
- Nonlinear Equations
(a) Newton-like Methods
(b) Unconstrained Optimization