Week 
Date 
Topic 
1 
8/28 
Introduction; matrix multiplication 
2 
8/31 
Caches and matrix multiply performance;
norms 

9/2 
Vector and matrix norms; perturbing
matrixvector multiply 

9/4 
Condition numbers; floating point 
3 
9/7 
Error analysis of quadratics and
matrixvector multiplies 

9/9 
Orthogonal matrices, SVD, low rank 

9/11 
Fast multiply, nonzero structure 
4 
9/14 
Timing matrix multiply; Gaussian
elimination 

9/16 
LU factorization and Schur
complements 

9/18 
Triangular solves, packed storage, block
LU 
5 
9/21 
Block LU with special blocks; perturbation
theory 

9/23 
Backward error in GE; pivoting; iterative
refinement 

9/25 
Iterative refinement; condition estimation;
scaling 
6 
9/28 
Symmetric matrices, LDL’, and
Cholesky 

9/30 
Stability of Cholesky; diagonal dominance;
sparse LU 

10/2 
Matrices and graphs; tree matrices; nested
dissection 
7 
10/5 
Normal equations, QR, GramSchmidt, and
reflections 

10/7 
Householder QR, storing Q and R, least
squares sensitivity 

10/9 
Sensitivity of y = A’*x and of least
squares 
8 
10/12 
Fall break — no lecture 

10/14 
Sensitivity redux; sparse least squares
problems 

10/16 
Constrained minimization, orthogonal
Procrustes, rankdeficiency 
9 
10/19 
Rankdeficient least squares; some
multivariate calculus reminders 

10/21 
Intro to eigenvalue problems 

10/23 
Firstorder sensitivity; intro to
Gershgorin 
10 
10/26 
Gershgorin and BauerFike 

10/28 
Power method, shiftinvert, RQ iteration, and
subspace iteration 

10/30 
Orthogonal iteration and QR 
11 
11/2 
Orthogonal iteration, QR, and Hessenberg
QR 

11/4 
Shift strategies for QR 

11/6 
Full implicit doubleshift QR with
deflation 
12 
11/9 
Rayleigh quotients, minimax and interlace
theorems 

11/11 
Interlace, inertia, and brief intro to
bisection 

11/13 
SVD algorithms (guest lecture by Charlie Van Loan) 
13 
11/16 
Introduction to the Lanczos
iteration 

11/18 
More Lanczos: reorthogonalization, error
estimates, convergence 

11/20 
Arnoldi; Krylov methods for Ax=b; stationary
methods; preconditioning 
14 
11/23 
Derivation of conjugate gradients 

11/25 
Thanksgiving special: a regression
puzzle 

11/27 
Thanksgiving recess — no lecture 
15 
11/30 
CG convergence; GMRES; a model
problem 

12/2 
Multigrid 

12/4 
