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
matrixvector 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,
GramSchmidt 

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 
Rankdeficiency 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 
Firstorder sensitivity; intro to
Gershgorin 

10/17 
Gershgorin and BauerFike 

10/19 
Power method, shiftinvert, 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 doubleshift 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 (rankstructured solvers) 

11/23 
Thanksgiving recess — no lecture 
15 
11/26 
Lanczos method for symmetric
eigenproblems 

11/28 
Lanczos, continued 

11/30 
Review 