====== 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