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Department:

MATH

Course Number:

6643

Hours - Lecture:

3

Hours - Lab:

0

Hours - Recitation:

0

Hours - Total Credit:

3

Typical Scheduling:

Every fall (MATH) and spring (CSE)

Introduction to the numerical solution of the classic problems of linear algebra including linear systems, least squares, SVD, eigenvalue problems. Crosslisted with CSE 6643.

Course Text:

Numerical Linear Algebra with Julia by Eric Darve, Mary Wootters

ISBN: 9781611976540

SIAM

Topic Outline:

- 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