| Date | Topic | Reference | Note |
|---|---|---|---|
| 0 | Introduction | Top 10 Algorithms in the 20th Century | |
| Matrix multiplication | |||
| 1 | Basic and block formulation |
BLAS LAPACK CLAPACK Prof. Demmel's talk | note01 |
| 2 | Parallel matrix multiplication | note02 | |
| 3 | Strassen algorithm |
note03_1, note03_2 | |
| 4 | Fast Fourier Transformation | note04 | |
| Sparse matrices |
Matrix Market Sparse Matrix Collection | hw1.pdf | |
| Basic matrix decomposition | |||
| 5 | LU decomposition and Cholesky decomposition | note05 | |
| 6 | QR decomposition: Gram-Schmidt process | note06 | |
| QR decomposition: Householder reflection | |||
| 7 | QR decomposition: Green's rotation | note07 | |
| Block version decompositions and parallelization | |||
| Eigenvalue problems | |||
| 8 | Eigenvalue problems: Power methods | note08 | |
| 9 | Eigenvalue problems: Orthogonal iteration | note09 | |
| 10 | Eigenvalue problems: QR method | note10 | |
| 11 | Symmtric eigenvalue problems and SVD | note11 | |
| Krylov subspace methods | |||
| 12 | Definition and theorems | note12 | |
| 13 | GMRES | note13 | |
| 14 | CG | cg | |