MTH 651: Advanced Numerical Analysis

Fall 2011




Instructor
Jay Gopalakrishnan
Venue
NH 8
Times
Tue, Thu: 12:00-13:15
Office hours
Tue 13:15-14:15 (in NH 309) or by appointment (email: gjay@pdx.edu).

Objective
Every mathematical scientist and engineer needs to work with matrices and vectors analytically and numerically. The course aims to teach often needed tools for computations with linear operators.

Outline
This is the first part of a three-part year-long advanced sequence on techniques for scientific computation. The three parts are loosely organized as follows:

  • Part 1: Numerical linear algebra
  • Part 2: Finite elements and finite differences
  • Part 3: Nonlinear techniques

Plan for this quarter (Part 1) :

  • SVD
    • Orthogonal and oblique projections. Singular value and other decompositions. Solution techniques for dense systems.
  • Iterative techniques
    • Conjugate Gradient algorithm, Arnoldi, Lanczos, and other Krylov space iterations, gmres, multigrid iteration, basic preconditioning techniques.

    (Eigenvalue algorithms moved to another term)


References
  1. Numerical Linear Algebra, by Lloyd N. Trefethen and David Bau III.
  2. Matrix Computations, by Gene H. Golub and Charles F. van Loan
  3. Iterative Methods for Sparse Linear Systems by Y. Saad

You are not required to buy any of these.


Evaluation
Grades will be assigned based on take-home projects. Projects can be computational or theoretical, and can be tailored to student background and preferences.

Jay Gopalakrishnan