| Class | Date | Topic | Reading | Assigned | Due |
|---|---|---|---|---|---|
| 1 | 1/5 | Preliminaries - Sources of error - Well-posedness - Conditioning - Stability - Floating point |
Heath, Chapter 1
Conditioning and Stability notes Floating Point notes |
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| 2 | 1/7 | HW1 | |||
| 3 | 1/9 | ||||
| 4 | 1/12 | Solving linear systems - Existence and Uniqueness of solutions - Vector and Matrix Norms - Sensitivity and conditioning | Heath, Chapter 2
Floating Point Math notes Norms, linear systems Matrix condition number |
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| 5 | 1/14 | HW2 | HW1 | ||
| 6 | 1/16 | ||||
| - | 1/19 | HOLIDAY | |||
| 7 | 1/21 | Matrix condition number - Solving linear systems - SPD systems - Cholesky factorization | Heath, Sections 2.3.3-2.3.5, 2.4, 2.5
Triangular systems Gaussian Elimination |
HW2 | |
| 8 | 1/23 | ||||
| 9 | 1/26 | Least squares - Orthogonality - Projectors - SVD - Overdetermined systems - QR decomposition | Heath Sections 3.1-3.6
GE with pivoting, Cholesky Orthogonality, SVD |
HW3 | |
| 10 | 1/28 | ||||
| 11 | 1/30 | ||||
| 12 | 2/2 | Eigenvalues and eigenvectors | Heath Sections 4.1, 4.2, 4.4, 4.5.1, 4.5.2, 4.5.4, 4.5.5 | HW3 | |
| 13 | 2/4 | ||||
| 14 | 2/6 | ||||
| 15 | 2/9 | Nonlinear Equations | Heath Sections 5.1-5.5.4, 5.5.7, 5.6.1-5.6.3 | ||
| 16 | 2/11 | ||||
| 17 | 2/13 | ||||
| - | 2/16 | HOLIDAY | |||
| 18 | 2/18 | Optimization - unconstrained - one-dimensional - multi-dimensional | Heath Sections 6.1, 6.2.2., 6.3, 6.4.1, 6.4.3, 6.5.2-6.5.6 | ||
| 19 | 2/20 | ||||
| 20 | 2/23 | Conjugate Gradients | An Introduction to the Conjugate Gradient Method Without the Agonizing Pain by Jonathan Richard Shewchuk | ||
| 21 | 2/25 | ||||
| 22 | 2/27 | ||||
| 23 | 3/2 | Polynomial Interpolation | Heath, Sections 7.3.1-7.3.3, 7.4 | ||
| 24 | 3/4 | ||||
| 25 | 3/6 | ||||
| 26 | 3/9 | Numerical Integration and Differentiation | Heath Sections 8.1, 8.2, 8.3.1, 8.3.3, 8.3.6, 8.4.3, 8.4.4, 8.6.1, 8.7 | ||
| 27 | 3/11 | Final | |||
| 28 | 3/13 | ||||
| - | 3/16 | FINALS WEEK | |||
| - | 3/18 | Take-home final | |||
| - | 3/20 |