MTH
451-
551
: NUMERICAL LINEAR ALGEBRA - Fall 2014
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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:
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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.
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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.
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