| 1 |
Introduction, Examples, Matrix-Vector and Matrix-Matrix Products |
|
| 2 |
Orthogonal Matrices, Norms of Matrices |
|
| 3 |
The Singular Value Decomposition |
|
| 4 |
QR Factorization |
|
| 5 |
Givens Rotations and Householder Reflections |
Homework 1 due |
| 6 |
Least Squares Problems |
|
| 7 |
Floating Point Arithmetic |
Homework 2 due |
| 8 |
Conditioning and Stability |
|
| 9 |
Stability of Givens Rotations and Backward Substitution |
Homework 3 due |
| 10 |
Stability of Least Squares Problems |
|
| 11 |
Gaussian Elimination |
|
| 12 |
Cholesky Factorization |
Homework 4 due |
| 13 |
Eigenvalue Problems |
|
| 14 |
Hessenberg Reduction |
Homework 5 due |
| 15 |
QR Algorithm |
|
| 16 |
Midterm |
Homework 6 due |
| 17 |
Stability of the QR Algorithm; Jacobi |
|
| 18 |
Bisection, Divide and Conquer |
|
| 19 |
SVD Algorithms |
|
| 20 |
Iterative Algorithms, Arnoldi |
Homework 7 due |
| 21 |
Lanczos, GMRES |
|
| 22 |
Conjugate Gradients |
Homework 8 due |
| 23 |
Solutions to Ordinary Differential Equations |
|
| 24 |
Runge Kutta Methods |
Homework 9 due |
| 25 |
Solutions to Stiff ODEs - I |
|
| 26 |
Solutions to Stiff ODEs - II |
Homework 10 due |