Numerical Linear Algebra

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.

Prerequisites: 

MATH 2406 or MATH 4305 or consent of School

Course Text: 

No text

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