Week |
Date |
Topic |
Homework/Test |
1 |
Mon Jan 14 |
Introduction |
The Definition of Numerical Analysis |
| Part I: Fundamentals |
Wed Jan 16 |
1: Matrix-Vector Multiplication |
|
|
Fri Jan 18 |
2: Orthogonal Vectors and Matrices |
Mathematical autobiography using the
Layout skill (LaTeX template) |
2 |
Mon Jan 21 |
Martin Luther King, Jr. Day, no class |
Wed Jan 23 |
3: Norms |
Problems 1.1 and 1.3 |
Fri Jan 25 |
4: The Singular Value Decomposition (video) |
Problems 2.2 and 2.6 (drop deadline) |
3 |
Mon Jan 28 |
5: More on the SVD |
Problem 3.3; Problem 3.4 using the Flow skill |
Wed Jan 30 |
| Part II: QR Factorization and Least Squares |
Fri Feb 1 |
6: Projectors |
Problems 4.1 and 4.2 |
4 |
Mon Feb 4 |
7: QR Factorization |
Problem 5.3 using the Graphs skill |
Wed Feb 6 |
8: Gram-Schmidt Orthogonalization |
Problems 6.2 and 6.4 |
Fri Feb 8 |
9: Matlab |
Problem 7.1 and 7.5 |
5 |
Mon Feb 11 |
10: Householder Triangularization |
Problems 8.1 and 8.2 |
Wed Feb 13 |
guide | Test on Part I |
Fri Feb 15 |
11: Least-Squares Problems |
Problems 9.1 and 9.3 |
6 |
Mon Feb 18 |
| Part III: Conditioning and Stability |
Wed Feb 20 |
12: Conditioning and Condition Numbers |
Problems 10.2 and 10.3 |
Fri Feb 22 |
13: Floating Point Arithmetic |
Problem 11.1 using the Logic skill; Problem 11.3 |
7 |
Mon Feb 25 |
14: Stability |
Problem 12.2 |
Wed Feb 27 |
15: More on Stability |
Problems 13.2 and 13.3 |
Fri Mar 1 |
guide |
Test on Part II |
Spring Break |
8 |
Mon Mar 11 |
16: Stability of Householder Triangularization |
Problem 14.1 using the Intros skill; Problem 14.2 |
Wed Mar 13 |
17: Stability of Back Substitution |
Problem 15.1 and 15.2 |
Fri Mar 15 |
9 |
Mon Mar 18 |
18: Conditioning of Least Squares Problems |
Problem 16.2 |
Wed Mar 20 |
19: Stability of Least Squares Algorithms |
Problem 17.1 using the
Symbols skill; Problem 17.2 |
Fri Mar 22 |
| (drop deadline with WP/WF) |
10 |
| Part IV: Systems of Equations |
Mon Mar 25 |
20: Gaussian Elimination |
Problems 18.1 and 18.2 |
Wed Mar 27 |
21: Pivoting |
Problem 19.1 as a good problem; Problem 19.2 |
Fri Mar 29 |
22: Stability of Gaussian Elimination |
Problems 20.1 and 20.5 |
11 |
Mon Apr 1 |
23: Cholesky Factorization |
Problems 21.1 and 21.6 |
Wed Apr 3 |
guide |
Test on Part III |
Fri Apr 5 |
12 |
| Part V: Eigenvalues |
Mon Apr 8 |
24: Eigenvalue Problems |
Problem 22.1 as a good problem. Presentations start. |
Wed Apr 10 |
25: Overview of Eigenvalue Algorithms |
Problems 23.1 and 23.3 |
Fri Apr 12 |
26: Reduction to Hessenberg or Tridiagonal Form |
Problems 24.1 and 24.4 |
13 |
Mon Apr 15 |
27: Rayleigh Quotient, Inverse Iteration |
Problems 25.1 and 25.3;
|
Wed Apr 17 |
28: QR Algorithm without Shifts |
Problem 26.1 |
Fri Apr 19 |
29: QR Algorithm with Shifts |
Problem 27.1 as a good problem; Problem 27.4 |
14 |
Mon Apr 22 |
30: Other Eigenvalue Algorithms |
Problems 28.2 and 28.3 |
Wed Apr 24 |
31: Computing the SVD |
Problem 29.1 |
Fri Apr 26 |
| Problems 30.1 and 30.3 |
15 |
Wed May 1 |
12:20 pm in our regular classroom |
Final Exam (guide) |