Applied Linear Algebra - Math-505

Direct solution of linear equations: Elimination and Factorization method, Ill-conditioning,, Iterative refinement. Orthogonal Factorizations: Jacobi method, Gauss-seidel method, SOR method, Conjugate Gradients method, Pre-conditioning, Chebyshev semi-iteration method. Matrix Eigenvalue Problems: Power method,  Inverse Power method, and Shifted Inverse Power method. Jacobi iterative method, Given's method, and Householder method. Sturm Sequence and QR method, Singular value decomposition.