Introduction to the numerical solution of the classic problems of linear algebra including linear systems, least squares, SVD, eigenvalue problems. Crosslisted with CSE 6643.
- Introduction - Standard problems, matrix factorizations, perturbation theory, round-off error, matrix and vector norms
- Solving Systems of Linear Equations - Perturbation theory, Gaussian elimination, error analysis, pivoting and stability, sparse systems
- Linear Least Squares Problems - Matrix factorizations: QR and SVD, perturbation theory, orthogonal matrices
- Eigenvalue Problems - Canonical forms, perturbation theory, nonsymmetric problems: power, inverse, orthogonal, QR iterations, symmetric problems: QR, Rayleigh Quotient \noindent Miscellaneous topics as time permits
- Iterative Methods for Solving Linear Systems - Poisson's equation, Jacobi, Gauss-Seidel, and SOR iterations, Krylov subspace methods, multigrid
- The Singular Value Decomposition and Generalized Inverse
- Functions of a Matrix