AMATH 584: Applied Linear Algebra and Introductory Numerical Analysis

SLN 10236, MWF 2:30-3:20, Loew Hall 216

Instructor:

Professor Loyce Adams
Guggenheim 415K
tel: 543-5077
fax: 685-1440
adams@amath.washington.edu
office hours: MWF 1:30-2:30 and 3:30-4:30 or by appt.

Teaching Assistant:

Alan Chen
Guggenheim 406
tel:
fax: 685-1440
email: mchen01@u.washington.edu
office hours: Tu 3:30-4:30, Th 2:20-3:20

Homework

Grades

Message Board

2008 Web Page

EDGE Streaming Video

Tutorials

Notes

Course description

Textbook

Syllabus

Objectives

Schedule

Course Description

This course is an introductory graduate level course in numerical methods designed to give engineering, mathematics, and science students the expertise necessary to understand and use computational methods for solving scientific problems. The emphasis is on methods for linear algebra problems (direct methods for linear systems, linear least squares problems, and algebraic eigenvalue problems). This course is the first in a series of three numerical methods courses. Amath 585 treats boundary value problems (ODEs and PDEs) and iterative methods for their numerical solution. Amath 586 treats initial value problems (ODEs), parabolic and hyperbolic PDEs and methods for their numerical solution. This is a five (5) credit course.

Prerequisites

Some Computing Programming Desirable (MATLAB or Fortran or C)
ODE's (AMATH 351, MATH 307, or equivalent)
Linear Algebra (MATH 308 or equivalent)

Recommended Preparation:
Proficiency in a computing language and familiarity with UNIX.

Computer Usage:
Need access to Matlab. Math Sciences Computer Center in Thompson Hall is an option.

Computer Software:
MATLAB, LAPACK.

Laboratory Projects:
Approximately five computer projects using numerical software.

Syllabus

1. Review of Applied Linear Algebra

(a) Change of basis, null space, range, rank

(b) Eigendecompositions, similarity transformations

(d) Special matrices: symmetric, orthogonal, permutation, projectors, lower and upper triangular, tridiagonal, banded, Hessenberg, Householder

2. Linear Least Squares Problems

(a) The Full Rank Case

i. Normal equations

ii. QR factorization approach

(b) The Rank Deficient Case

i. QR with pivoting

ii. The SVD and the minimum norm solution

3. Other Applications of the SVD

(a) The null space problem

(b) Image processing

4. Numerical Approximation and Computation Errors

(a) Truncation error

(b) Floating point arithmetic, machine epsilon

(d) Ill-conditioning, stability

5. Direct Methods for Solving Dense Systems of Linear Equations

(a) Gaussian elimination with partial pivoting

(b) Cholesky decomposition, A=LDL^T for symmetric matrices

(d) Software: LAPACK, NETLIB, MATLAB

6. Direct Methods for Solving Sparse Structured Systems of Linear Equations

(a) Tridiagonal systems

(b) Banded systems

7. The Algebraic Eigenvalue Problem

(a) The Power and Inverse Power methods

(b) QR algorithm

(d) Software: LAPACK, NETLIB, MATLAB

8. Systems of Nonlinear Equations

Textbooks

Trefethen, L. & Bau, D. Numerical Linear Algebra. SIAM Publishing, 1997. Available at the University Bookstore.

Schedule and Homework

Follow links in the table below to obtain a copy of the homework in PostScript (.ps) or Adobe Acrobat (.pdf) format. You may also obtain here solutions to some of the homework and exam problems. An item shown below in plain text is not yet available. For additional information regarding viewing and printing the homework and solution sets, click here.

Homework and Exams	Homework Due Date	Homework Problem Sets	Homework Selected Solutions
First day of classes	Wednesday, September 30
Homework#1	Mon, Oct 12	(.ps), (.pdf)	HW #1 Solutions (hw1_soln.pdf)
Homework#2	Wed, Oct 21	(.ps), (.pdf)	HW #2 Solutions (hw2_soln.pdf)
Homework#3 - Part 1	Fri, Oct. 30, 2009	(.ps), (.pdf), HW 3 Matlab File: clgs.m , HW 3 Matlab File: mgs.m , HW 3 Matlab File: ellipse.m ,	HW #3 Solutions (hw3_soln.pdf)
Homework#3 - Part 2	Fri, Oct. 30, 2009	(.ps), (.pdf)
Homework#4	Fri, Nov. 20, 2009	(.ps), (.pdf)
Homework#5	Mon, Dec 7, 2009	(.ps), (.pdf)