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IAM 961 course outline

We will follow Trefethen and Bau's text pretty closely, chapter by chapter. Here's a slightly different conceptual organization of the course than provided by Trefethen and Bau's table of contents, with rough dates. By the end of the semester, you should have a pretty good grasp of each of the topics mentioned herein.

Fundamentals, Sept 1 – 22

  • orthogonality, norms, SVD
  • Trefethen lectures 1 – 5

Direct methods, Sept 24 – Oct 22

  • QR factorization: Gram-Schmidt and modified Gram-Schmidt algorithms, Householder algorithm, least squares
  • conditioning, stability, and accuracy
  • LU decomposition (a.k.a. Gaussian elimination), pivoting
  • Trefethen chapters 6-23

Iterative methods, Oct 27 – Nov 26

  • eigenvalue algorithms: Rayleigh quotient, inverse iteration, QR algorithm, shifts
  • SVD algorithms
  • Krylov subspace methods: Arnoldi iteration, GMRES, and conjugate gradients
  • Trefethen chapters 24-40

Optimization, (time permitting) Dec 1 – Dec 10

  • Newton's method, trust-region modifications
gibson/teaching/fall-2014/iam961/outline.txt · Last modified: 2014/09/09 10:10 by gibson