CS 515: Numerical Linear Algebra

List of Topics:

Part I: Dense Matrix Computation

Direct Linear System Solvers

Hours Topic
2 LU and Cholesky factorization schemes
2 Norms and condition numbers
3

Pivoting strategies, scaling, and iterative refinement

Least Squares Problems
2 Orthogonal projections
3 Orthogonal factorization schemes -- Givens, Householder, and Gram-Schmidt
3

Singular-value decomposition

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

Hours Topic
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

Total Hours: 43

Last Updated: Jun 20, 2025 1:29 PM