The following course schedule is tentative, and may be changed.

Week Date Topic
1 8/22 Introduction; matrix multiplication
8/24 Caches and matrix multiply performance; norms
2 8/27 Vector and matrix norms; perturbing matrix-vector multiply
8/29 Condition numbers; floating point
8/31 Error in dot products; forward and backward error
3 9/3 Labor day — no lecture
9/5 Orthogonal matrices, SVD, low rank
9/7 Fast multiply, nonzero structure
4 9/10 Gaussian elimination
9/12 Schur complements and blocked factorization
9/14 Backward error in GE; pivoting; iterative refinement
5 9/17 Condition estimation and scaling
9/19 Guest lecture: CVL
9/21 Guest lecture: CVL
6 9/24 Matrices and graphs; tree matrices; nested dissection
9/26 Normal equations, QR, Gram-Schmidt
9/28 Householder reflections, Givens rotations, and QR
7 10/1 Sensitivity of y = A’*x and of least squares
10/3 Sensitivity redux; sparse least squares problems; pivoting
10/5 Rank-deficiency and regularized least squares
8 10/8 Fall break — no lecture
10/10 Intro to eigenvalue problems
10/12 Applications of eigenvalues
9 10/15 First-order sensitivity; intro to Gershgorin
10/17 Gershgorin and Bauer-Fike
10/19 Power method, shift-invert, RQ iteration, and subspace iteration
10 10/22 Orthogonal iteration and QR
10/24 Orthogonal iteration, QR, and Hessenberg QR
10/26 Shift strategies for QR
11 10/29 Full implicit double-shift QR with deflation
10/31 Rayleigh quotients, minimax and interlace theorems
11/2 Interlace, inertia, and brief intro to bisection
12 11/5 Classical stationary iterations
11/7 Kronecker products and the 2D model problem
11/9 Convergence of classical iterations on the model problem
13 11/12 Chebyshev acceleration and Krylov subspaces
11/14 Derivation of conjugate gradients
11/16 More on CG
14 11/19 CG convergence
11/21 Thanksgiving special (rank-structured solvers)
11/23 Thanksgiving recess — no lecture
15 11/26 Lanczos method for symmetric eigenproblems
11/28 Lanczos, continued
11/30 Review