Math 504 (Fall 2018) - Lecture Notes

Math 504 - Lecture Notes

Week 1 (Background)

Week 2 (Singular Value Decomposition)

Week 3 (Applications of Singular Value Decomposition & Projectors)

Week 4 (Orthogonal Projectors)

Weeks 5-6 (QR Factorization by Householder Reflectors)

Week 7 (Least Squares Problem)

Week 8 (LU Factorization, Conditioning, Stability)

Week 9 (LU Factorization with Partial Pivoting)

Week 10 (Computation of One Eigenvalue)

Week 11 (Computation of All Eigenvalues)

Week 12 (Computation of Singular Values)

Week 13 (Krylov Subspace Methods: GMRES, Arnoldi's Method)

pdf notes used in the lectures

Lecture 2

Lecture 3

Lecture 4

Lecture 5

Lecture 6

Lecture 7

Lecture 8

Lecture 9

Lecture 10

Lecture 11

Lecture 12

Lecture 13 --- Fitting a polynomial to data

Lecture 14

Lecture 15 --- Pseudocode for LU factorization

Lecture 16

Lecture 17 --- Matrix Norms

Lecture 18

Lecture 19

Lecture 20

Lecture 21

Lecture 22 -- Pseudocode to Compute Eigenvalues

Lecture 23

Lecture 24

Lecture 25

Lecture 26