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