Schedule

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 |
||

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 |
||

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 |