Numerical Linear Algebra
Math-6316 and CSE-7366
Spring 2009
Instructor: Dr. Yunkai Zhou
Phone: 214-768-2512, Email: yzhou@smu.edu
Lecture: Tue & Th, 11:00 am -- 12:30 pm, Clements Hall 224
Office hours: Tue, 3:30--5:30pm; Fri, 3:00-5:00pm (Clements 132)
- Course description:
This course will cover the development and analysis of numerical linear algorithms
used in the solution of linear equations,
eigenvalue problems, and linear least-square problems.
It will also cover the Conditioning (related to the problems) and Stability
(related to the algorithms) issues.
Both dense methods and sparse methods will be discussed.
The emphasis will be dense methods.
[ Prerequisites:
Basic knowledge of matrix theory and linear algebra; basic knowledge of
computer programming. ]
- Educational outcomes:
Students will be able to master theoretical properties related to
important matrix decompositions including QR, LU, Eigen-decomposition, and SVD.
They will also be able to understand why these decompositions are important,
what are their applications, and what are the main ideas behind the standard
numerical algorithms used to compute these decompositions.
Students will be able to correctly code certain standard numerical algorithms
for solving linear equations, least square problems, and eigenvalue problems.
-
Textbooks:
Lloyd N. Trefethen
and David Bau ,
Numerical Linear Algebra,
SIAM, 1997. ISBN: 0-89871-361-7;
- Supplementary textbooks:
- Gene Golub and
Charles Van Loan ,
Matrix computations, 3rd Ed.,
Johns Hopkins University Press, 1996. ISBN: 0-8018-5414-8
- G. W. Stewart ,
Matrix algorithms I: Basic decompositions,
SIAM, 1998. ISBN: 0-89871-414-1
G. W. Stewart,
Matrix algorithms II: Eigensystems,
SIAM, 2001. ISBN: 0-89871-503-2
- Yousef Saad ,
Iterative methods for sparse linear systems , SIAM, 2003.
ISBN-13: 978-0-898715-34-7.
[1st edition]
- J. Demmel ,
Applied numerical linear algebra, SIAM, 1997. ISBN: 0-89871-389-7
-
Henk A. Van der Vorst ,
Iterative Krylov methods for large linear systems,
Cambridge University Press, 2003, ISBN: 0521818281.
Lecture notes on large linear systems and eigenvalue problems
- D. S. Watkins ,
Fundamentals of matrix computations, 2nd Ed.,
Wiley-Interscience, 2002. ISBN: 0-471-21394-2
-
Nicholas J. Higham ,
Accuracy and Stability of Numerical Algorithms, SIAM, 2002. SBN: 0-89871-521-0.
- C. Moler,
Numerical Computing with MATLAB, SIAM, 2004. ISBN-13: 978-0-898715-60-6
[electronic version]
- C. D. Meyer ,
Matrix Analysis and Applied Linear Algebra, SIAM, 2000.
[online version]
- Software: the commercial
Matlab
and/or the open sourceware
Scilab ,
Octave .
-
Further Readings of interest:
-
Course Policy:
- Class attendance is required (unless with permission from the instructor)
- Homework due dates are specified on the webpage
- Homework counts 65% in total
- Midterm and final count 35%