Math 929 - Iterative Methods in Linear Algebra

Outline

Linear Algebra

A brief overview and review of some linear algebra results, and a short discussion of some direct methods.
  1. Condition number of a matrix. Spectral radius.
  2. LU factorization (Gaussian elimination).
  3. QR factorization.
  4. Eigenvalue solvers.

Symmetric matrices

The classical iterative methods, and conjugate gradient.
  1. Jacobi and Gauss-Seidel.
  2. SOR method.
  3. Conjugate gradient method.
  4. Lanczos iteration.

Nonsymmetric matrices

The hot area....
  1. CGNR - conjugate gradient applied to the normal equations.
  2. GMRES and GMRES(k).
  3. CGS, BCGS, BiCGSTAB, etc....

Odds and ends

Preconditioning, Multigrid, nonlinear problems.