| LEC # | LECTURE NOTES | SUPPLEMENTARY FILES |
|---|---|---|
| 1 | Introduction, Basic Linear Algebra (PDF) 6 slides per page (PDF) | |
| 2 | Orthogonal Vectors and Matrices, Norms (PDF) 6 slides per page (PDF) | Vector Norms lec2mldemo1.m (M) Induced Matrix Norms lec2mldemo2.m (M) |
| 3 | The Singular Value Decomposition (PDF) 6 slides per page (PDF) | |
| 4 | The QR Factorization (PDF) 6 slides per page (PDF) | |
| 5 | Gram-Schmidt Orthogonalization (PDF) 6 slides per page (PDF) | Classical and Modified Gram-Schmidt lec5mldemo1.m (M) clgs.m (M) mgs.m (M) |
| 6 | Householder Reflectors and Givens Rotations (PDF) 6 slides per page (PDF) | Householder QR Factorization house.m (M) formQ.m (M) |
| 7 | Least Squares Problems (PDF) 6 slides per page (PDF) | |
| 8 | Floating Point Arithmetic, The IEEE Standard (PDF) 6 slides per page (PDF) | Floating Point Arithmetic lec8mldemo1.m (M) num2bin.m (M) |
| 9 | Conditioning and Stability I (PDF) 6 slides per page (PDF) | |
| 10 | Conditioning and Stability II (PDF) 6 slides per page (PDF) | |
| 11 | Gaussian Elimination, The LU Factorization (PDF) 6 slides per page (PDF) | LU Factorization lec11mldemo1.m (M) lec11mldemo2.m (M) mkL.m (M) mkP.m (M) |
| 12 | Stability of LU, Cholesky Factorization (PDF) 6 slides per page (PDF) | |
| 13 | Eigenvalue Problems (PDF) 6 slides per page (PDF) | |
| 14 | Hessenberg / Tridiagonal Reduction (PDF) 6 slides per page (PDF) | |
| 15 | The QR Algorithm I (PDF) 6 slides per page (PDF) | |
| 16 | The QR Algorithm II (PDF) 6 slides per page (PDF) | Jacobi Algorithm lec16mldemo1.m (M) jacrot.m (M) |
| 17 | Other Eigenvalue Algorithms (PDF) 6 slides per page (PDF) | Method of Bisection lec17mldemo1.m (M) sturmcount.m (M) Divide-and-Conquer Algorithm lec17mldemo2.m (M) |
| 18 | The Classical Iterative Methods (PDF) 6 slides per page (PDF) | |
| 19 | The Conjugate Gradients Algorithm I (PDF) 6 slides per page (PDF) | Conjugate Gradients cg.m (M) cg_stats.m (M) |
| 20 | The Conjugate Gradients Algorithm II (PDF) 6 slides per page (PDF) | Conjugate Gradients lec20mldemo1.m (M) steep.m (M) conjdir.m (M) conjgrad.m (M) |
| 21 | Sparse Matrix Algorithms (PDF) 6 slides per page (PDF) | Elimination Movie lec21mldemo1.m (M) realmmd.m (M) |
| 22 | Preconditioning, Incomplete Factorizations (PDF) 6 slides per page (PDF) | |
| 23 | Arnoldi / Lanczos Iterations (PDF) 6 slides per page (PDF) | Arnoldi Iteration arnoldi.m (M) |
| 24 | GMRES, Other Krylov Subspace Methods (PDF) 6 slides per page (PDF) | |
| 25 | Linear Algebra Software (PDF) 6 slides per page (PDF) |