AMATH 584
SLN 1217, MWF 2:30-3:20, GUGGENHEIM HALL 217 **** changed from earlier

Applied Linear Algebra and Introductory Numerical Methods

Instructor:

Professor Loyce Adams
Guggenheim 408L
tel: 543-5077
fax: 685-1440
adams@amath.washington.edu
office hours: MWF: 1:30-2:30, T,Th: Appt.

Teaching Assistant:

David George
Guggenheim Hall
tel:
fax: 685-1440
dgeorge@amath.washington.edu
office hours: Tu, Th, 1:30-2:30
MATLAB HELP: Email him for a time.

Homework

Grades

Message Board

2003 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, algebraic eigenvalue problems) and methods for ordinary differential equations (the initial value problem). This course is the first in a series of three numerical methods courses. This is a five (5) credit course.

Prerequisites

FORTRAN or C programming
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

9. ODEs - The Initial Value Problem--(Instructor's Notes)

(a) Issues of stability, convergence, consistency, stepsize control

(b) Euler's method, Trapezoid method

(d) Software: NAG, NETLIB, LSODE

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 Solutions
First day of classes	Wednesday, September 29
Homework#1	Friday, Oct 15	(.ps), (.pdf)
Homework#2	Monday, Oct 25	(.ps), (.pdf)
Homework#3	Fri, Nov. 5, 2004	(.ps), (.pdf), HW 3 Matlab File: clgs.m , HW 3 Matlab File: mgs.m ,
Exam # 1	Mon, Nov. 8, 2004	(.ps), (.pdf),	It is now posted!
Homework#4	Mon., Nov. 22 , 2004	(.ps), (.pdf), HW 4 Matlab File: ellipse.m ,
Homework#5	Wed., Dec 1 , 2004	(.ps), (.pdf)
Veteran's Day	Thursday, November 11	No class
Thanksgiving Break	Th-Fri, November 25-26	No class
Final - Part 1	Fri., Dec 10 , 2004	(.ps), (.pdf)
Final - Part 2	Tuesday, Dec 14 , 2004	(.ps), (.pdf)
Last day of classes	Friday, December 10

Grading

Computer projects and homework: 50%, midterm: 25%, final: 25%. You may view your homework and exam grades on-line. Before doing so for the first time, you must request a password. Please note this change to our system: Your student ID number should be entered including any leading zeros (e.g. 0012345).