Math 614: Numerical Linear Algebra --- Fall 2017
To contact the instructor: j.rhodes@alaska.edu
Course syllabus: M614syl.pdf
Required Textbook: Numerical Linear Algebra, by Lloyd N. Trefethen and David Bau, III, 1997 / xii + 361 pages / Softcover / ISBN: 978-0-898713-61-9 / List Price $67.00 / SIAM Member Price $46.90
Note: Students may join SIAM (the Society for Industrial and Applied Mathematics) for $25, or for free if they are among the first two to ask the instructor for a nomination. Even at $25, the cost is almost offset by the discount price for the text, and comes with lots of other benefits as well. See SIAM Student Membership.
Homework Assignments:
The dates below are when problems were assigned. Unless otherwise noted, problems are always due the following Monday.
Homework should be typed, in LaTeX,following the template HWtemplate.tex.
Problems are from T&B, unless otherwise stated.
- 8/28 1.1, 1.2, #1 Let A=[2 1 1; -2 0 1; 4 4 6], b=[1; -4; -4]. By hand solve Ax=b. Compute rank, determinant, inverse(if possible), and eigenvalues of A. Verify your results with MATLAB
- 8/30 none
- 9/1 1.4
- 9/4 LABOR DAY
- 9/6 2.1, 2.2, 2.3, 2.4, #1 Show the product of unitary matrices is unitary.
- 9/8 2.6, 2.7, 3.1, 3.2
- 9/11 3.3, 3.4, 3.5, #1 Show any matrix norm induced from vector norms is actually a norm (i.e., satisfies the defiinition given in equations 3.1 (or 3.15) of the text.
- 9/13 4.1, #2 Use appropriate MATLAB command to find the singular value and eigen decompositions of A=[3 1 0; 0 2 1; 0 0 1] and B=[1 1 0; 0 1 1; 0 0 1]. One of these 4 results should be wrong or produce an error message. Which one, and why?
- 9/15 4.2, 4.4
- 9/18 5.1, 5.3, 5.4
- 9/20 6.1, 6.2, 6.3
- 9/22 6.4, 6.5
- 9/25 7.1, 7.2, 7.5, #1 Continue orthonormalizing Legendre polynomials as in class, finding Q_2, P_3, and Q_3.
- 9/27 9.1
- 9/29 8.3, 10.1, 10.2 (turn in MATLAB code and example of run on the matrix in 10.3)
- 10/2 none
- 10/4 11.3, #1(a) If Sigma is diagonal and mxn of full rank n, what is the pseudoinverse Sigma^+? Justify your answer. (b) If A is mxn of full rank n and has svd U\Sigma V*, what is the svd of A^+? Justify your answer.
- 10/6 12.1, 12.2
- 10/9 none
- 10/11 none
- 10/13 none
- 10/16 MIDTERM EXAM
- 10/18 13.2ab, 13.3, 14.1a-c,e-g
- 10/20 15.1a-d,15.2
- 10/23
- 10/25
- 10/27