List of Topics: Hours Topics Part I: Dense Matrix Computation 1. Direct linear system solvers 2 LU and Cholesky factorization schemes 2 Norms and condition numbers 3 Pivoting strategies, scaling, and iterative refinement 2. Least squares problems 2 Orthogonal projections 3 Orthogonal factorization schemes -- Givens, Householder, and Gram-Schmidt 3 Singular-value decomposition 3. The symmetric eigenvalue problem 2 Eigenvalues and eigenvectors 2 Power method and inverse iteration 2 Reduction to the tridiagonal form 2 Extraction of eigenpairs Part II Iterative methods for sparse linear systems 2 Discretization of partial differential equations 2 Sparse matrices 2 Basic iterative linear system solvers 3 Projection methods 5 Krylov subspace methods 2 Schemes for normal equations 4 Preconditioning techniques 43 hours total 2003.08