Catalog Description

This course is a survey of numerical methods in linear algebra for application to problems in engineering and the sciences.  Emphasis is on using modern software tools on high performance computing systems.  This course covers the mathematics of linear equations, eigenvalue problems, singular value decomposition, and least squares.  Material covered will be relevant to application areas such as structural analysis, heat transfer, neural networks, mechanical vibrations, and image processing in biomedical engineering.  A familiarity with Matlab is useful, and the ability to program in languages such as C/C++ or Fortran is very important. A basic knowledge of matrix algebra is required. Prerequisite: MTH 253 or 355, and CS 142 or 241.   4 credit hours.

Text Books

1. Primary: Datta, B. N., Numerical Linear Algebra and Applications, Brooks/Cole Publishing Co., 1995, ISBN 0-534-17466-3.

2.  Reference: Golub, G. H. and Van Loan, C. F., Matrix Computations, Third Edition, The Johns Hopkins University Press, 1996, ISBN 0-8018-5414-8.

Home Page

http://www.cs.wright.edu/people/faculty/rtaylor/ceg416.html

Course Goals

The student should have learned the following:

1. Methods for solution of linear equations and least squares problems
2. Solutions techniques for algebraic eigenvalue and singular value problems.
3. Understand convergence and stability of numerical methods.
4. Understand current mathematical software and areas of engineering application.

The student should be able to apply the concepts above to the following:

1. Stable and accurate solutions of linear equations that are dense or have special structure.
2. Computation of eigenvalues, singular values and vectors of matrices that are dense or have special structure.
3. Stable and accurate least squares solutions to data fitting problems.
4. Design numerical solution techniques applicable to large-scale engineering problems.

Prerequisites by Topic

1. Ability to program in C/C++, Fortran, or Java
2. Familiarity with Matlab on PCs or Unix computers.
3. Ability to understand and apply matrix operations and concepts at an intermediate level.
4. Understanding of general areas of engineering application.

Major Topics Covered in the Course

Homework and Project Assignments

There are a total of six Homework/Projects assignments are made during the quarter.  These include text problems and numerical experimentation with Matlab.  Standards for presentation of computational mathematics solutions are given on the course web site.  At least one assignment includes the review of a paper on a topic such as floating point arithmetic or selected engineering/numerical linear algebra applications

Estimate CSAB Category Content

Oral and Written Communications

There are no oral presentations.  Students submit source code of their homework/projects along with written documentation.  Each assignment must contain a written summary of the assignment.  Discussion is encouraged in class and occasionally a student may be asked to present a solution of a problem to the class.

Social and Ethical Issues

None specifically; however, lectures do include significant comment on the importance of writing quality software which as been thoroughly tested and checked.  For example, structural or civil engineering programs must be based on numerical algorithms that are stable and accurate when applied to design and analysis of bridges and earthquake resistant buildings.

Theoretical Content

About two weeks total is spent on relating computational material to basic concepts learned in applied linear or matrix algebra courses.  Since matrix computation does require a significant mathematical background, more or less time may be spent depending on the particular interests and capabilities of the students.  The theoretical content of the course is also justified since about one third to one half of the students in a typical class are registered as graduate mathematics students.

Problem Analysis

Homework and projects include selected open-ended exercises that require numerical experimentation with algorithms.  For example, when iterative methods do not converge for certain matrix eigenvalue problems, students are required to analyze the theoretical basis of the method and examine workable modifications to algorithms to handle special cases.

Solution Design

Design experience is necessarily related to algorithm design.  Programs developed by students must be designed in a modular form and use of object-oriented features in Matlab is encouraged.