MATH 629 (04888), Winter 2010

Numerical Analysis: Linear Algebra

Catalog Description:
In-depth analysis of numerical aspects of problems and algorithms in linear algebra.
Desired Learning Outcomes:
Students will have a deep understanding of numerical methods for linear algebra. They will know the standard methods and be able to analyze and learn new methods on their own.
Prerequisites:
MATH 511 & (544 OR 546). 511 is to ensure you know about matrices, vector spaces, etc. 544 or 546 is to ensure you have some experience with computers, and how to make them do numerical calculations. If you would like to take this course, but do not formally meet the prerequisites, please contact me.
Instructor:
Martin J. Mohlenkamp, mohlenka@ohio.edu, (740)593-1259, 315B Morton Hall.
Office hours: Monday 3:10-4pm, Tuesday 3:10-4pm, Thursday 3:10-4pm, and Friday 3:10-4pm.
Web page:
http://www.ohio.edu/people/mohlenka/20102/629.
Class hours/ location:
MTuThF 2:10-3pm in 313 Morton Hall.
Text:
Numerical Linear Algebra, by Lloyd N. Trefethen and David Bau III. Society for Industrial and Applied Mathematics, 1997; ISBN 978-0-898713-61-9. (Become a student member of SIAM and buy it through them at a discount.) (The first 5 lectures are available online.)
Homework:
From each section of the book, two or so homework problems will be assigned, to be turned in two classes after we finish that section. Most problems are paper-and-pencil problems, but some require (Matlab) programming. One problem each week will be designated a "Good Problem", which means it must
Tests:
There will be three mid-term tests, in class.
Final Exam:
The final exam is on Wednesday, March 17, at 12:20 pm in our regular classroom.
Presentation:
Toward the end of quarter, you will be assigned one section of the book to formally present to the class, as if it was a seminar talk.
Grade:
Your grade is based on homework at 40%, three tests at 10% each, a presentation at 10%, and the final exam at 20%. An average of 90% guarantees you at least an A-, 80% a B-, 70% a C-, and 60% a D-. Grades are not the point.
Attendance:
Attendance and participation is very important in this course, since the learning model is based on group in-class activities. I do not count attendance in your grade, since absences will penalize you through your loss of learning.
Academic Dishonesty:
On the homework you may use any help that you can find, but you must acknowledge in writing what help you received and from whom or where. The tests and final exam must be your own work, and without the aid of notes, etc. Dishonesty will result in a zero on that work, and possible failure in the class and a report to the university judiciaries.
Special Needs:
If you have specific physical, psychiatric, or learning disabilities and require accommodations, please let me know as soon as possible so that your learning needs may be appropriately met.
Learning Resources:
  • Your classmates are your best resource. Use them!
  • LaTeX, Python, and Matlab resources.
  • Wikipedia's Numerical Analysis pages and the (skeletal) Wikiversity course on Numerical Linear Algebra.
  • Schedule

    Subject to change. Further homework problem numbers to be announced.
    Week Date Topic Homework/Test
    1 January 4 Introduction The Definition of Numerical Analysis
    Part I: Fundamentals
    January 5 1: Matrix-Vector Multiplication
    January 7 2: Orthogonal Vectors and Matrices Mathematical autobiography using the Layout skill (LaTeX template)
    January 8 3: Norms Problems 1.1 and 1.3
    2 January 11 4: The Singular Value Decomposition Problems 2.2 and 2.6
    January 12
    January 14 5: More on the SVD Problems 3.3 and 3.4
    January 15
    3 January 18 Martin Luther King, Jr. Day, no class
    Part II: QR Factorization and Least Squares
    January 19 6: Projectors Problem 4.1; Problem 4.2 using the Flow skill (drop deadline)
    January 21 7: QR Factorization Problem 5.3
    January 22 Problems 6.2 and 6.4
    4 January 25 Test on Part I
    January 26 8: Gram-Schmidt Orthogonalization
    January 28 9 Matlab Problem 7.1 and 7.4
    January 29 10: Householder Triangularization Problem 8.2; Problem 8.1 using the Logic skill
    5 February 1 11: Least-Squares Problems Problems 9.1 and 9.3
    February 2
    Part III: Conditioning and Stability
    February 4 12: Conditioning and Condition Numbers Problems 10.2 and 10.3
    February 5 13: Floating Point Arithmetic Problems 11.1 and 11.3
    6 February 8 (drop deadline with WP/WF)
    February 9 Test on Part II
    February 11 14: Stability
    February 12 15: More on Stability Problem 12.2 using the Graphs skill
    7 February 15 Problems 13.2 and 13.3
    February 16 16: Stability of Householder Triangularization Problems 14.1 and 14.2
    February 18 17: Stability of Back Substitution Problem 15.1 and 15.2
    February 19
    8 February 22 18: Conditioning of Least Squares Problems Problem 16.2 using the Intros skill
    February 23 Problems 17.1 and 17.2
    February 25 19: Stability of Least Squares Algorithms
    Part IV: Systems of Equations
    February 26 20: Gaussian Elimination
    9 March 1 Problems 18.1 and 18.2
    March 2 21: Pivoting Problems 19.1 and 19.2
    March 4
    March 5 Test on Part III
    10 March 8 22: Stability of Gaussian Elimination (Presentation) Problems 20.1 and 20.3
    March 9 23: Cholesky Factorization (Presentation) Problems 21.1 and 21.6
    Part V: Eigenvalues
    March 11 24: Eigenvalue Problems (Presentation) Problem 22.1 using the Symbols skill
    March 12 Problems 23.1 and 23.3
    11 March 17 Wednesday at 12:20 pm in our regular classroom Final Exam

    Martin J. Mohlenkamp
    Last modified: Fri Sep 3 13:54:54 EDT 2010