MTH 451- 551 : NUMERICAL LINEAR ALGEBRA - Fall 2014
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General information
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Instructor: Malgorzata Peszynska
[Office hours: please check Instructor's homepage.]
Class: MWF 10:00-10:50 MLM 234

Course information: Credits: 3.00.
Course content:
  • Numerical solution of linear systems using direct methods, factorizations and decomposition of matrices.
  • Stability and accuracy of numerical methods for linear algebra.
  • Orthogonal decompositions, SVD (singular value decomposition) and least squares.
  • Numerical methods for finding eigenvalues and eigenvectors.
  • Iterative methods for solving linear systems and in particular positive definite systems.
Additional topics and applications will be developed as time permits.

Student preparation: good background in linear algebra (MTH 341 or equivalent is a prerequisite.) Familiarity with (some) numerical methods, algorithms, some programming language, and in particular with MATLAB is a plus; however, I will develop the basics as necessary. [From catalogue: programming experience or instructor approval required. MTH 342 and MTH 351 are recommended.]
Exams: There will be two exams: a midterm (in class) in week 4 (friday October 24) and a Final Exam. Each exam will count as 30% of the grade.
Grading: Homework will count as 40% of the grade and will be assigned (almost always) weekly.

Textbook and materials:

NUMERICAL LINEAR ALGEBRA
Lloyd N. Trefethen and David Bau, III
xii+361 pages; SIAM, 1997
Softcover / ISBN-13: 978-0-898713-61-9 / ISBN-10: 0-89871-361-7 /

MATLAB: there exist plenty of good resources for MATLAB, some available online (search, for example, for "matlab tutorial free"). Depending on class needs, we may schedule (some) class(es) in a lab in the first few weeks.

I start by looking at a 2 by 2 matrix. Sometimes I look at a 4 by 4 matrix. That's when things get out of control and too hard. Usually 2 by 2 or 3 by 3 is enough, and I look at them, and I compute with them, and I try to guess the facts.
Paul R. Halmos
Course Learning Outcomes:
A successful student who completed MTH 451 will be able to
  • Understand and use basic direct methods for solving linear systems
  • Implement and justify convergence of simple iterative methods for solving linear systems
  • Follow analyses of stability and accuracy of an algorithm, and determine accuracy experimentally
  • Propose an appropriate method for a given linear system and desired decomposition of a given matrix
A successful student who completed MTH 551 will be able to
  • Analyze and test selected direct methods for solving linear systems
  • Implement and analyze convergence of selected iterative methods for solving linear systems
  • Carry out analyses of stability and accuracy of an algorithm, and determine accuracy experimentally
  • Propose an appropriate method for solving a linear system or for decomposition of a matrix of typical category.

Course drop/add information is at http://oregonstate.edu/registrar/. Special arrangements for students with disabilities: please contact Services for Students with Disabilities prior to or during the first week of the term to discuss accommodations. Students who believe they are eligible for accommodations but who have not yet obtained approval through DAS should contact DAS immediately at 737-4098.
Course drop/add information is at http://oregonstate.edu/registrar/.
Student Conduct: All students are expected to obey to OSU’s student conduct regulations, see OSU’s Statement of Expectations for Student Conduct . See also Academic or Scholarly Dishonesty link.