Math 630 - Numerical Linear Algebra

Spring 2021 - Syllabus - 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.

This course will also include computational work to gain practical experience with the numerical methods discussed. I recommend the professional software package Matlab or equivalently the free and nearly fully compatible package Octave as platform of choice, because they are very popular packages and knowing them thoroughly is itself a marketable skill. For both packages, you can read its expansive and well-written documentation or you may consider the book recommended above. For hands-on training in Matlab and Octave, you can consider the 2-credit class Math 426 on Matlab or for a brief initial overview the software workshops offered by CIRC.

Learning Goals

By the end of this course, you should:

Other Information

Note on Recordings and Their Publication

This class is being audio-visually recorded so students who cannot attend a particular session and wish to review material can access the full content. This recording will include students' images, profile images, and spoken words, if their camera is engaged and their microphone is live. Students who do not consent to have their profile or video image recorded should keep their camera off and not use a profile image. Likewise, students who do not consent to have their voice recorded should keep their mute button activated and participate exclusively through alternative formats such as email or the chat feature (where available).

UMBC Statement of Values for Academic Integrity

Academic integrity is an important value at UMBC. 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. Consult the the UMBC webpage on Academic Integtrity at for the UMBC Undergraduate Student Academic Conduct Policy for undergraduate students and the UMBC Graduate School's Policy and Procedures for Student Academic Misconduct for graduate students.

Copyright © 1999-2021 by Matthias K. Gobbert. All Rights Reserved.
This page version 1.0, December 2020.