CME 302/CS 237A. Numerical Linear Algebra

Institute for Computational and Mathematical Engineering
and the Department of Computer Science
Stanford University
Fall 2007

This course is the first in a three quarter graduate sequence designed to acquaint students in mathematical and physical sciences and engineering with the fundamental theory of numerical analysis. This first course is devoted to the solution of systems of linear equations, covering the following topics: direct methods, error analysis, structured matrices, iterative methods, least squares, parallel techniques.

Announcements

• The first problem set is posted.
• The second problem set is posted.
• Note the new email address for communication with TAs.
• Office hours for the week of Monday, Oct. 22 will be held by appointment only.

Logistics

Location: McCullough Building, Room 115

Times: 11:00 AM–12:15 PM on Mon/Wed/Fri. Please see Lectures for dates.

Course staff

Instructor: Gene Golub (golub@stanford.edu).
Gates Building 2B, Room 280
(650) 723-3124

Teaching assistants:

• Please send all course related email to cme302-cas@lists.stanford.edu.
• Nick Henderson (nwh@stanford.edu).
• Chris Maes (cmaes@stanford.edu).

• Monday, 7-9pm (Durand)
• Tuesday, 4-6pm (Durand)
• Wednesday, 7-9pm (in 320-221)
• Thursday, 7-9pm (Durand)

Topics

• Introduction

• Matrix analysis

• Inexact computation

• Direct methods for the solutions of linear systems

• Least squares problems

• Iterative methods

Lectures

Homework assignments

• Problem Set 1 (pdf, tex)---Due Friday October 5th, at 5 PM outside of Durand 112. You are encouraged to LaTeX your solutions.
• Problem Set 2 (pdf, tex)---Due Friday October 19th, at 5PM outside of Durand 112. You are encouraged to LaTeX your solutions. Note: This problem set is lengthy, please start early!
• Problem Set 3 (pdf, tex) ---Due Friday November 9th, at 5PM outside of Durand 112. You are encouraged to LaTeX your solutions.
• Problem Set 4 (pdf, tex) ---Due Friday November 30th, at 5PM outside of Durand 112. You are encouraged to LaTeX your solutions.
• Final Exam (pdf, tex) ---Due Friday December 14th, at 5PM outside of Durand 112. Please note that no collabration is allowed and that no late work will be accepted.

Grades

A grade will be assessed on about four to five homework sets and a take-home final exam.

Notes

Recommended texts

• G. Golub and C. Van Loan, Matrix computations, 3rd Ed., Johns Hopkins Series in the Mathematical Sciences, 3, Johns Hopkins University Press, Baltimore, MD, 1996. ISBN: 0-8018-5414-8

• L.N. Trefethen and D. Bau, Numerical linear algebra, SIAM, Philadelphia, PA, 1997. ISBN: 0-89871-361-7

• J. Demmel, Applied numerical linear algebra, SIAM, Philadelphia, PA, 1997. ISBN: 0-89871-389-7 (before you buy this book, you might want to check this out)

Supplementary texts

• D.S. Bernstein, Matrix mathematics, Princeton University Press, Princeton, NJ, 2005. ISBN: 0-691-11802-7

• Å. Björck, Numerical methods for least squares problems, SIAM, Philadelphia, PA, 1996. ISBN: 0-89871-360-9

• N.J. Higham, Accuracy and stability of numerical algorithms, 2nd Ed., SIAM, Philadelphia, PA, 2002. ISBN: 0-89871-521-0

• G.W. Stewart, Matrix algorithms I: basic decompositions, SIAM, Philadelphia, PA, 1998. ISBN: 0-89871-414-1

• G.W. Stewart, Matrix algorithms II: eigensystems, SIAM, Philadelphia, PA, 2001. ISBN: 0-89871-503-2

• H.A. van der Vorst, Iterative Krylov methods for large linear systems, Cambridge Monographs on Applied and Computational Mathematics, 13, Cambridge University Press, Cambridge, UK, 2003. ISBN: 0-521-81828-1

• D. Watkins, Fundamentals of matrix computations, 2nd Ed., Wiley-Interscience, New York, NY, 2002. ISBN: 0-471-21394-2

Stuff you may find interesting

• PDF files of Demmel's book (we disavow any knowledge of their existence)

• Trefethen's list of 13 classic papers in applied mathematics

• Using linear algebra to identify important jurisprudence

• Using linear algebra to rank web pages

Software

• Netlib
• LAPACK
• LINPACK
• EISPACK
• FISHPACK

• ATLAS

• Mathworks

Reference books for programming

• C. Moler, Numerical computing with MATLAB, SIAM, Philadelphia, PA, 2004. ISBN 0-89871-560-1 (this book is freely available online at http://www.mathworks.com/moler)

About this page

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