| Lecture | Date | Topic | Reading |
|---|---|---|---|
| 1 | 9/23 | Linear algebra review: span, linear dependence, bases, matrices, matrix-vector multiplication, matrix-matrix multiplication, column space, rank, outer product matrices | Solomon 1.1-1.3 |
| 2 | 9/28 | Floating-point number representation, Sources of error, Conditioning, stability, accuracy |
Solomon 2.1-2.3
Heath 1.2-1.3 |
| 3 | 9/30 | ||
| 4 | 10/5 | Linear systems, Existence and uniqueness of solutions, LU factorization |
Solomon 3.1-3.5
Heath 2.1-2.2, 2.4 |
| 5 | 10/7 | ||
| 6 | 10/12 | Special linear systems, positive definite matrices, sparse matrices Matrix and vector norms, sensitivity analysis |
Solomon 4.2-4.3
Heath 2.5, 2.3 |
| 7 | 10/14 | ||
| 8 | 10/19 | Orthogonality, orthonormal set of vectors, orthogonal matrix Projections, Gram-Schmidt, modified Gram-Schmidt, Householder transformations |
Solomon 5.1-5.6
Heath 3.5 |
| 9 | 10/21 | ||
| - | 10/26 |
Review session
Thursday - MIDTERM |
|
| - | 10/28 | ||
| 10 | 11/2 | Eigenvectors, characteristic polynomial, Power iteration, inverse power iteration, shifting QR iteration, Krylov subspace methods |
Solomon 6.1-6.5
Heath 4.1, 4.4-4.5 |
| 11 | 11/4 | ||
| 12 | 11/9 |
Singular Value Decomposition and applications
Thursday - HOLIDAY |
Solomon 7.1-7.2
Heath 4.7 |
| - | 11/11 | ||
| 13 | 11/16 | Nonlinear systems, root finding, fixed point iteration, Newton's method, single variable, convergence rates |
Solomon 8.1-8.3
Heath 5.1-5.6 |
| 14 | 11/18 | ||
| 15 | 11/23 |
Systems of nonlnear equations, Newton's method for systems, Unconstrainted optimization, optimality
Thursday - HOLIDAY |
Solomon 9.1
Heath 6.1-6.2.2 |
| - | 11/25 | ||
| 16 | 11/30 |
Tuesday - Review Session
Thursday - FINAL | |
| 17 | 12/2 |