COSC 3362: Numerical Methods II

Course Information

Lectures:	4 - 5:30 pm in 347 Phlip G. Hoffman Hall
Instructor:	Dragan Mirkovic
E-mail:	mirkovic@cs.uh.edu
Office:	221 Phlip G. Hoffman Hall
Office Hours:	TTH 9 - 10:30 pm

Course Description

Numerical solutions of problems in linear algebra; systems of linear equations, matrix inversion, and eigen-value problems.

Prerequisites:

COSC 1301, 1410, or 2101, and MATH 2431.

Texts

Required:	Numerical Analysis - Mathematics of Scientific Computing, by David R. Kincaid and E. Ward Cheney. 3rd Edition This highly successful and scholarly book introduces students with diverse backgrounds to the various types of mathematical analysis that are commonly needed in scientific computing. The subject of numerical analysis is treated from a mathematical point of view, offering a complete analysis of methods for scientific computing with careful proofs and scientific background.

Recommended:	Afternotes on Numerical Analysis, by G. W. Stewart This book presents the central ideas of modern numerical analysis in a vivid and straightforward fashion with a minimum of fuss and formality. Stewart designed this volume while teaching an upper- division course in introductory numerical analysis. To clarify what he was teaching, he wrote down each lecture immediately after it was given. The result reflects the wit, insight, and verbal craftmanship which are hallmarks of the author. Simple examples are used to introduce each topic, then the author quickly moves on to the discussion of important methods and techniques. With its rich mixture of graphs and code segments, the book provides insights and advice that help the reader avoid the many pitfalls in numerical computation that can easily trap an unwary beginner. Written by a leading expert in numerical analysis, this book is certain to be the one you need to guide you through your favorite textbook.

Topics covered

Introduction
Solving Systems of Linear Equations.

Matrix Algebra.
LU and Cholesky Factorizations.
Pivoting and Constructiong an Algorithm.
Norms and the Analysis of Errors.
Neumann Series and Iterative Refinement.
Solution of Equations by Iterative Methods.
Steepest Descent and Conjugate Gradient Methods.
Analysis of Roundoff Error in the Gaussian Algorithm.

Selected Topics in Numerical Linear Algebra.

Review of Basic Concepts.
Matrix Eigenvalue Problem: Power Method.
Schur's and Gershogorin's Theorems.
Orthogonal Factorizations and Least-Squares Problems.
Singular-Value Decomposition and Pseudoinverses.
QR-Algortihm of Francis for the Eigenvalue Problem.

Evaluation

The homework assignments will not be graded. You will have to demonstrate your knowledge and understanding of these problems, though, by solving the similar problems in quizzess (approx. 2/month).

Projects (4)	25%
Quizzes (6)	20%
Midterm Exam	25%
Final Exam	30%
Course grades posted

Projects

Date	Topic	Reference	Due
03/29/2005	Solution of linear systems (ps) (pdf)	TBA	04/12/2005

Quizzes

There will be two or three quizzes per month, depending on the number of lectures and other assignments. Each quiz will have two problems related to the recently covered material and you will have 15 min to solve them at the begining of the class. Here is the quiz schedule (subject to change).

Date	Topic	Reference
02/10/2005	Matrix Algebra and LU Factorization	Ch. 4.1-4.3

Class Schedule

Date	Topic	Handout	Homework
1/20/2005	Course Overview and Introduction	Syllabus	None
1/25/2005	Matrix Algebra	None	Read Ch. 4.1
1/27/2005	LU and Cholesky Factorizations	None	Read Ch. 4.2 Problems: 1, 4, 5, 6, 7, 47 pp. 158
2/01/2005	Pivoting	None	Read Ch. 4.3 Problems: 1, 9, 18, and 28 pp. 180
2/08/2005	Matrix norms	None	Read Ch. 4.4 Problems: 15, 16, and 40 pp. 193
2/15/2005	Iterative refinement	None	Read Ch. 4.5 Problems: 11, 19, and 26 pp. 205
3/8/2005	Review	Sample Midterm Exam (ps) (pdf)	TBA
3/11/2005	Midterm Exam	None	TBA
3/21/2005	Iterative Methods	None	Read Ch. 4.6 Problems: pp. 239
3/29/2005	Steepest Descent and Conjugate Gradient Methods	None	Read Ch. 4.7 Problems: 7, 13, pp. 244
4/5/2005	# Matrix Eigenvalue Problem: Power Method	None	Read Ch. 5.1 Problems: 7, 13, pp. 244

Final Exam

The final exam of COSC 3362 is scheduled for Thurs, May 12, 5-8 pm.

Final Exam Reading List

Introduction

Academic Integrity

You are expected to maintain the utmost level of academic integrity in the course. Any violation of the code will be penalized severely. You are not allowed to collaborate on the homework assignments except for discussing the assignment with other students in the class. You are not allowed to share code or any other written material.

Dragan Mirkovic