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