| Lecture | Date | Topic | Reading |
|---|---|---|---|
| / | 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 | |
| / | Floating-point number representation, Sources of error, Conditioning, stability, accuracy |
Solomon 2.1-2.3
Heath 1.2-1.3 |
|
| / | |||
| / | Linear systems, Existence and uniqueness of solutions, LU factorization |
Solomon 3.1-3.5
Heath 2.1-2.2, 2.4 |
|
| / | |||
| / | Special linear systems, positive definite matrices, sparse matrices Matrix and vector norms, sensitivity analysis |
Solomon 4.2-4.3
Heath 2.5, 2.3 |
|
| / | |||
| / | Orthogonality, orthonormal set of vectors, orthogonal matrix Projections, Gram-Schmidt, modified Gram-Schmidt, Householder transformations |
Solomon 5.1-5.6
Heath 3.5 | |
| / | |||
| - | / |
Review session
Thursday - MIDTERM |
|
| - | / | ||
| / | 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 |
|
| / | |||
| / |
Singular Value Decomposition and applications
Thursday - HOLIDAY |
Solomon 7.1-7.2
Heath 4.7 |
|
| - | / | ||
| / | Nonlinear systems, root finding, fixed point iteration, Newton's method, single variable, convergence rates |
Solomon 8.1-8.3
Heath 5.1-5.6 |
|
| / | |||
| / |
Systems of nonlnear equations, Newton's method for systems, Unconstrainted optimization, optimality
Thursday - HOLIDAY |
Solomon 9.1
Heath 6.1-6.2.2 |
|
| - | / | ||
| / |
Tuesday - Review Session
Thursday - FINAL | ||
| / |