MAT 263 - Computational Linear Algebra

Course Objectives

1. To learn numerical solutions of linear systems,
2. To solve numerically eigenvalue-eigenvector problems,
3. To analyze convergence of iterative methods,
4. To solve linear algebra problems with popular programming languages,

Course Description

The concepts of vector and matrix norms, positive definite matrix, linear independence, dimensions and bases. Solution of linear systems: Direct methods (Gauss-Elimination, Gauss-Jordan, pivoting, Cramer methods, LU, Cholesky and QR decompositions), Iterative methods (Jacobi and Gauss-Seidel methods, Successive over relaxation method) and convergence analysis, Solutions of linear systems with popular programming languages. Eigenvalue and eigenvector problems: Gerschgorin disks, Rayleigh quotient, Trace method, Power and inverse power methods and power method with shifting. Solutions of eigenvalue-eigenvector problems with popular programming languages. Singular value decomposition.