Math 630 - Numerical Linear Algebra

Spring 2014 - Matthias K. Gobbert

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Basic Information

Course Description

This course encompasses basic theory of matrices and numerical methods for computations with matrices including both their theory and implementation in a computer.

One prototypical example of a problem in linear algebra concerns the solution of a system of simultaneous linear equations. Gaussian elimination (also known as reduction to row echelon form) is the traditional computational technique for its solution, both in hand-calculations and in a computer. Using it as an example, we will learn what might be necessary to make a computational technique reliable and efficient in a computer and what analytical results can be developed for a numerical method. To analyze the problems and numerical methods, we will introduce basic tools including vector and matrix norms.

Gaussian elimination is an example of a direct method (that produces the solution in a predetermined number of steps). We will also consider iterative methods (that find successively better approximations to solution as more steps are taken) and their advantages and drawbacks. In addition to system of linear equations, we will study least-squares and eigenvalue problems, and various numerical methods to solve them. Their analysis will require a review of various facts about matrices including the theory of eigenvalues and the singular value decomposition as well as the development of a number of other computational techniques.

We will involve the professional software package Matlab in several ways: We will use it to extend hand-calculations to larger examples, its scripting language will serve as a programming environment for our own code, and we will spend time understanding how some of the numerical methods discussed in class are implemented in Matlab's functions.

Learning Goals

By the end of this course, you should:

Other Information

UMBC Academic Integrity Policy

By enrolling in this course, each student assumes the responsibilities of an active participant in UMBC's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. Cheating, fabrication, plagiarism, and helping others to commit these acts are all forms of academic dishonesty, and they are wrong. Academic misconduct could result in disciplinary action that may include, but is not limited to, suspension or dismissal. To read the full Student Academic Conduct Policy, consult the UMBC Student Handbook, the Faculty Handbook, the UMBC Integrity webpage, the UMBC Undergraduate Student Academic Conduct Policy (PDF) for undergraduate students, or the University of Maryland Graduate School, Baltimore (UMGSB) Policy and Procedures for Student Academic Misconduct (PDF) for graduate students.

Copyright © 1999-2014 by Matthias K. Gobbert. All Rights Reserved.
This page version 1.1, January 2014.