MATH 6640 (3509-100), Spring 2013

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.
Requisites:
MATH 5600 Introduction to Numerical Analysis
Instructor:
Martin J. Mohlenkamp, mohlenka@ohio.edu, (740)593-1259, 315B Morton Hall.
Office hours: Monday, Wednesday, and Friday 2:00-2:55pm, or by appointment.
Web page:
http://www.ohiouniversityfaculty.com/mohlenka/20132/6640.
Class hours/ location:
Monday, Wednesday, and Friday 3:05-4pm 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.) (Preview)
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 May 1 at 12:20 pm in our regular classroom.
Presentation:
Toward the end of semester, 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.
    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 guideTest 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)
    Martin J. Mohlenkamp
    Last modified: Mon Apr 22 09:32:51 EDT 2013