MA 614

Numerical Methods for Linear Algebra. Spring 2016.

Class materials

First day handout

Computer Problems rules:

When submitting an assignment, please ensure that (i) everything you expect me to read is in the hardcopy, and (ii) your assignments (without plots) are submitted to mark.pekker@uah.edu. Please, observe also the following:

• Do not print out numbers with very long fractions unless specifically asked to do so. For accuracy checking, print errors, not solution and approximate solution values. To display data or solution tendencies etc. use plots, not long lists of numbers.
• Running a program: use the MATLAB command 'diary' to accumulate your results in a file: type help diary. Edit the diary file and put brief statements and comments in your own words of what the results mean (just like writing a technical report about your finding). Highlight (or underline) your statements and comments and key relevant info from your results.
• When submitting programs, use separate files for separate Matlab functions (Function Programs and/or Script Programs).

Your write-ups must conform to the following template; the order of material is NOT optional:

• Description of the problem;
• A self-contained description of results and/or Summary table and/or graphs of results and associated comments;
• All Code listings (Appendix I) and all Raw output (this can be your edited diary file) (Appendix II).

Course info.

1. Introduction (Parts of Chapter 2). Standard problems, general techniques, review of some linear algebra, floating point arithmetic.

Homework 1  Due M. Jan. 25.  Problems (pp. 116 - 122): 2.1.10; 14 for p = 1,2,inf; 23; 28; 30.
Homework 2  Due M. Feb. 1.   Problems (pp. 126 - 148): 2.2.11 (not to hand in); 12; 15; 2.5.7; 2.5.9; 2.5.10.
Homework 3  Due W. Feb. 10. Computing Project: project1-16.pdf.

2. Systems of linear equations (Parts of Chapters 1, 2): perturbation theory, Gaussian elimination and its variations, error analysis, special linear systems.
Homework 4.  Due M.  Feb 22. Problems (p. 100): 1.8.10, (p. 164): 2.7.16a, HW4-16.pdf.

3. The Linear least squares problem (Chapter 3): orthogonal matrices, projection, solution of the least squares problem; Gram-Scmidt process, QR decomposition.
Homework 5.  Due M. March 7. Problems (pp. 239 - 245) 3.5.2, 3.5.5, 3.5.28, 3.5.29; (p. 224) 3.4.3, 3.4.5.

4. The Singular value decomposition (Chapter 4): SVD, Applications to the least squares problem.
Homework 6.  Due W. March 16Problems (pp. 263 - 273) 4.1.13 - 4.1.16,  4.2.8, 4.2.14, 4.2.17, 4.2.20, 4.2.22

5. The Linear least squares problem (Chapter 3): orthogonal matrices, Gram-Scmidt process, QR decomposition.
Homework 7. Due M. March 28. Problems (pp. 189 - 235) 3.2.5, 3.2.8, 3.2.28 (c),(d),(e); 3.4.28 (a), (b), (d) (computer project); Prove that ||QAP||_2=||A||_2, where Q,A,P are n-by-n, and Q, P are orthogonal.

6. Eigenvalues and Eigenvectors (Chapter 5, Parts of Chapter 6): Canonical forms, algorithms, perturbation theory.
Homework 8. Due W. April 6. Problems (p. 308) 5.2.14, HW8a-16.pdf.
Homework 9. Due W. April 13. Problems (pp. 317 - 321) 5.3.8,  5.3.9,  5.3.10,  5.3.18; HW9a-16.pdf. For MATLAB problems email me your m-files and reports, along with hard copies.
Homework 10. Due W. April 20. HW10-16.pdf.

Supplementary materials

Self-contained basic MATLAB (Chapra)

MATLAB Tutorial (Ed Overman)

Basic MATLAB read from: MATLAB Tutorial (Ed Overman)

1.7 Script M- les . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.1 Anonymous Functions . . . . . . . . . . . . . .. . . . . . . .  . . . .. . 40
3.2 Passing Functions as Arguments . . . . . . . . . . . . . . . .. . 41

8 Programming in MATLAB . . . . . . . . . . . . . . . . . . . ..  . . . . . 91
8.1 Flow Control and Logical Variables . . . . . . . . . . . . . . . . 91
8.2 Matrix Relational Operators and Logical Operators . . 96
8.3 Function M- les . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . .  .. 100
8.4 Odds and Ends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Matt Dunham and Kevin Murphy https://code.google.com/p/yagtom/

Mathworks MATLAB Tutorials and Learning Resources

C. B. Moler, Numerical Computing with MATLAB

MATLAB primer

Crash Course in MATLAB, by Tobin Driscoll, University of Delaware