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) |