MATH 446 (04745), Spring 2009

Numerical Linear Algebra

Catalog Description:
Floating point arithmetic, numerical solution of systems of linear equations using Gaussian elimination and its variants, numerical techniques for eigenvalues, error analysis, and implementation of algorithms on computer.
Desired Learning Outcomes:
Students will be able to:
  • Utilize algorithms to solve common problems in linear algebra.
  • Analyze the accuracy of such algorithms.
  • Analyze the computational cost and efficiency of such algorithms.
  • Identify the sources of failure of such algorithms, and avoid them.
  • Prerequisites:
    MATH 410/510 and programming experience.
    Instructor:
    Martin J. Mohlenkamp, mohlenka@ohio.edu, (740)593-1259, 315B Morton Hall.
    Office hours: Monday 9:10-10am, Tuesday 9:10-10am, Thursday 9:10-10am, and Friday 9:10-10am.
    Web page:
    http://www.ohio.edu/people/mohlenka/20093/446-546.
    Class hours/ location:
    MTuThF 10:10-11am in 314 Morton Hall.
    Text:
    Numerical Analysis, 8th edition by Richard L. Burden and J. Douglas Faires; Brooks/Cole, 2004 ISBN: 0534392008. This book has online programs.
    We will also use Wikipedia's Numerical Analysis pages and background material borrowed from MATH 344.
    Homework:
    There will be weekly homework assignments, consisting of: You may work together in a group of two or three and submit a joint solution.
    Tests:
    There will be three mid-term tests, in class. Calculators are permitted for arithmetic.
    Project:
    Your project during the quarter is to critique and improve Wikipedia's Numerical Analysis pages. At the end of the quarter you will submit a written report and give a presentation on what you did.
    Final Exam:
    The final exam is on Thursday, June 11, at 8:00am in our regular classroom. Calculators are permitted for arithmetic.
    Grade:
    Your grade is based on homework 40%, tests 30%, final exam 20%, and project 10%. An average of 90% guarantees you at least an A-, 80% a B-, 70% a C-, and 60% a D-.
    Missed or Late work:
    Late homework is penalized 5% for each 24 hour period or part thereof, excluding weekends and holidays. You can resubmit homework to improve your score, but the late penalty will apply.
    Attendance:
    Attendance is not counted in your grade. However, you should estimate that for each class you miss your average will decrease by one point due to the learning you missed. It is your responsibility to find out any announcements made in class.
    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.
  • MATH 546 (04761)

    For students enrolled in MATH 546, the above syllabus is modified as follows:

    Homework:
    You must turn in an individual solution.
    Tests and Final Exam:
    Expect an additional, harder problem, such as a proof.
    Project:
    Your project is to add or extend a lesson on Wikiversity for Numerical Analysis or Numerical Algorithms.

    Schedule

    Subject to change.
    Week Date Topic/Materials Homework/Test
    Text Wikipedia Other
    1 March 30 Introduction 344: 1, 2, 3, 4, 5
    Direct Methods for Solving Linear Systems
    March 31 6.1 System of linear equations; Gaussian elimination 344: 8, 9, 10
    April 2 6.2 Pivoting 344: 11
    April 3 6.3 Linear algebra; Invertible matrix
    2 April 6 6.4 Determinant Homework 1, using Layout
    April 7 6.5 LU decomposition 344: 12
    April 9 6.6 Diagonally dominant matrix; Positive-definite matrix; Cholesky decomposition; Band matrix; Tridiagonal matrix
    April 10
    Iterative Techniques in Matrix Algebra
    3 April 13 7.1 Norm; Normed vector space; Matrix norm Homework 2, using Flow (drop deadline)
    April 14
    April 16 study guide Test on Chapter 6
    April 17 7.2 Eigenvalue, eigenvector and eigenspace; Characteristic polynomial; Spectral radius
    4 April 20 7.3 Jacobi method; Gauss-Seidel method; Successive over-relaxation
    April 21 7.4 Condition number Homework 3, using Logic
    April 23
    April 24 7.5 Conjugate gradient method
    5 April 27
    Approximating Eigenvalues
    April 28 9.1 Eigenvalue, eigenvector and eigenspace; Linear independence; Orthonormal basis; Orthogonal matrix; Unitary matrix; Similar matrix; Gershgorin circle theorem 344: 14 Homework 4, using Symbols
    April 30
    May 1 study guide Test on Chapter 7
    6 May 4 (drop deadline with WP/WF)
    May 5 9.2 Power iteration; Inverse iteration 344: 16
    May 7
    May 8 9.3 Householder transformation; Hessenberg matrix Homework 5, using Graphs
    7 May 11 9.4 Rotation matrix; Givens rotation; QR algorithm; QR decomposition 344: 17
    May 12
    Numerical Solutions of Nonlinear Systems of Equations
    May 14 10.1 Fixed point; Contraction mapping; Jacobian matrix Homework 6, using Intros
    May 15
    8 May 18 study guide Test on Chapter 9
    May 19 10.2 Newton's method 344: 13
    May 21 10.3 Quasi-Newton method; Broyden's method; Sherman-Morrison formula
    May 22
    9 May 25 Memorial Day, no class
    May 26 10.4 Gradient descent
    May 28 10.5 Homotopy
    May 29 Homework 7 due
    10 June 1 Project presentations
    June 2 Project presentations
    June 4 Project presentations
    June 5 Review Project reports due
    11 June 11 Thursday at 8:00am in our regular classroom study guide Final Exam

    Martin J. Mohlenkamp
    Last modified: Fri Sep 3 13:54:43 EDT 2010