Department of Computer Science and Engineering Wright State University

CEG 416 Matrix Computations

Catalog Data

[4 credit hours] Survey of numerical numerical methods in linear algebra emphasizing practice with high-level computer tools. Topics include Gaussian elimination, LU decomposition, numerical eigen-value problems, QR factorization, least squares, singular value decompositions, and iterative methods. Prerequisites: MTH 253 or 355 and CS 142 or 241.

Text Books and Other Source Materials 1. G. H. Golub and C. F. van Loan, Matrix Computations, 2nd edition, John Hopkins, 1989, ISBN 0-471-29288-5. 2. R.D.Skeel and J. D. Keiper, Elementary numerical computing with Mathematica, McGraw-Hill, 1993.

Coordinator Abdul Ahad S. Awwal, Associate Professor of Computer Science and Engineering

Schedule

Each week has two lectures of 75-minutes each. There is no scheduled lab. Students are expected to work in open labs for no less than 2 hours a week.

Prerequisites by Topic 1. Linear equations and transformation. 2. Algebraic eigenvalue problem. 3. Programming with arrays, functions and libraries 4. Logic and basic mathematical proof. 5. Application software: e.g. Matlab, maple 6. Matlab tools.

Course Content Wk Topics Read 1 Linear algebra review GvN1.1,1.2:1-5,2.1,SK4.1 2 Matrix and vector norms, singular values GvN2.2,2.3:1-3,2.5, SK4.2.1 GvN 2.4:2- 3 Floating point computation; condition numbers 4,2.6:1,2.7:1,2.7:3,SK4.2:2-3 GvN:3.1:1-2,3.1:8,3.2:1- 4 The LU decomposition 2,3.2:4-8, SK4.31-2 GvN 3.3:2,3.4:1-4,SK 5 Partial Pivoting 4.4:1,4.5:1-2 GvN3.4:10;4.1(Thm4.1.1 & 6 The Cholesky decomposition 4.1.2);4.2:1,4.2:3 GvN5.2:1-4;5.1:6,5.1:8- 7 Reflections and rotations 9,5.1:11 8 QR factorization GvN 5.2:1,5.2:3,5.2:6-7 9 Least Square problems and the normal equations GvN5.3:1-5 SR 6.1,6.2,6.3.2 10 Eigenvalues, diagonalization and schur decompositions GvN 7.1, Handouts 11 The QR iteration GvN 7.1, Handouts

Learning Objectives and Desired Outcomes

The student should have learned the following: 1. Understand linear equation methods 2. Understand eigenvalues and singular values 3. Geometric insight into matrix problems 4. Understand formulation of least squares 5. Understand convergence of iterative methods 6. Ability to adapt and apply math software

The student should be able to apply the concepts above to the following: 1. Solve equations by variations of Gauss method. 2. Solve equation by LU and Cholesky decomposition 3. Solve sparse and bounded equations 4. Solve the symmetric eigenvalue problem 5. Use of iteration for equation and eigenvalues 6. Use of QR and Jacobi transformation methods 7. Solve singular value problem 1. Solve the unsymmetric eigenvalue problem 2. Appreciation of parallel processing 3. Solve least square problem 4. Analysis of methods using norms 5. Analysis of convergence of methods 6. Ability to select correct methods for problems Outcome Measures and Assessment Student progress in achieving the desired objectives and outcomes for this course will be monitored and measured through use of entrance and exit surveys, programming assignments, homework, quizzes, examinations, and success in the courses that use CEG 320 as a prerequisite.

092398v1.2 Department of Computer Science and Engineering Wright State University

CEG 416 Matrix Computations

Assessment of Prerequisites Entrance Survey

Fall 1998, Section 01. Your Name (optional): ______

The following survey is being conducted at the entrance, during the first week of classes. Results from the collected data are used to improve how our courses are conducted. Please complete as well as you can. Please feel free to attach in a separate sheet any comments that you may have.

This course depends on material taught in the prerequisite courses listed. We would like to learn if you have the background that we expect for this course as shown in the prerequisites listed by topic in Table 2. Please give us the instructor's name so that we may give him/her this feedback.

Table 1: Prerequisites by Courses (circle the one that applies)

Taken at Term/Year Instructor's Name Grade MTH 253 or MTH 355

CS 142 or CS 241

Please assess how well you were prepared by assigning to yourself a letter grade (A, B, C, D, or F) to each of the prerequisite topics listed.

Table 2: Prerequisites by Topic Prerequisite Topic Grade Linear equations and transformation. Algebraic eigenvalue problem. Programming with arrays, functions and libraries Logic and basic mathematical proof. Application software: e.g. Matlab, maple Matlab tools. Department of Computer Science and Engineering Wright State University

CEG 416 Matrix Computations

Assessment of Learning Objectives and Desired Outcomes Exit Survey

Fall 1998, Section 01. Your Name (optional): ______

The following survey is being conducted during the final week of classes. Results from the collected data are used to improve our courses. Please feel free to attach a separate sheet of comments.

This course has the learning objectives listed below. In your opinion, how well did the course accomplish its objectives? Please fill in a letter grade (A, B, C, D, or F). Table 1: Learning Objectives

Understand linear equation methods Understand eigenvalues and singular values

Geometric insight into matrix problems

Understand formulation of least squares Understand convergence of iterative methods

Ability to adapt and apply math software

This course has the following desired outcomes. In your opinion, how well did the course accomplish these? Please fill in a letter grade (A, B, C, D, or F).

Table 2: Desired Outcomes

Solve equations by variations of Gauss method. Solve equation by LU and Cholesky decomposition

Solve sparse and bounded equations

Solve the symmetric eigenvalue problem

Use of iteration for equation and eigenvalues

Use of QR and Jacobi transformation methods

Solve singular value problem

Solve the unsymmetric eigenvalue problem

Appreciation of parallel processing

Solve least square problem

Analysis of methods using norms

Analysis of convergence of methods

Ability to select correct methods for problems Department of Computer Science and Engineering Wright State University

CEG 416 Matrix Computations

Program Outcomes and Assessment of a Single Course

Table of Criteria 3: Students who have successfully completed the course have

a1 an ability to apply knowledge of mathematics PXX

a2 an ability to apply knowledge of science PX

a3 an ability to apply knowledge of engineering PX

b1 an ability to design and conduct experiments 0

b2 an ability to analyze and interpret data X

c an ability to design a system, component, or process to meet desired 0 needs

d an ability to function on multi-disciplinary teams 0

e an ability to identify, formulate, and solve engineering problems PX

f an understanding of professional and ethical responsibility 0

g an ability to communicate effectively 0

h the broad education necessary to understand the impact of engineering 0 solutions in a global and societal context

i a recognition of the need for, and an ability to engage in life-long learning X

j a knowledge of contemporary issues 0

k an ability to use the techniques, skills, and modern engineering tools PX necessary for engineering practice Supporting Statements a1: Background in matrix methods and notation is used. Students must understand complex numbers and be able to follow basics of mathematical proofs. a2: Example applications are drawn from physics: mostly classical mechanics. a3: Example applications are from area of engineering mechanics including structural analysis and computational fluid mechanics. b2: Background in data analysis if useful in least square topics. e: Foundation of matrix equation in a manner compatible with the numerical methods is a useful skill and discussed. i: Ability to keep up with developing parallel processing (for example) is important. k: Experience with the use of software such as Matlab and maple for solving engineering problem is assumed but not required.