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