U.C. Berkeley Math 221 Home Page
Matrix Computations / Numerical Linear Algebra
MWF 11-12, 2 Evans Hall
564 Soda Hall ("Virginia"), (510)643-5386
831 Evans Hall
Office Hours - T 10:30-11:30 (changed as of Sep 16), Th 1-2, F 1-2 in 564 Soda
The reader for Ma221 is Nick Knight
Roxana Infante / Tammy Johnson
Offices: 563 / 565 Soda Hall
Phones: (510)643-1455 / (510)643-4816
(11/2) The due date for Homework 9 is extended until Nov 5.
(10/29) I posted an updated version of
at 9am today.
(10/23) Answers for HW 5, 6 and 7 are posted at
(10/12) A correction for HW 6, Question 3.17, p. 137, has been posted in the
List of Errata
(9/30) I just posted HW 5, and answers for HW 4.
(9/24) I just posted a new version of the HW 2 answers on bcourses with some minor corrections. I also posted HW 3 answers.
(9/21) I just posted a new version of the HW 1 answers on bcourses with some minor corrections.
(9/17) I'd like to pass on a request from the grader to please write neatly (if you turn in hand-written homework). If the grader can't read your writing without a great effort, then you may not get all the credit you should have gotten.
(9/16) Starting today, my Tuesday office hours will be 10:30-11:30.
(9/15) Answers to Homework 1 have been posted at
. Future homework answers will also be posted there.
(9/7) Question 1.5 is about vector norms, a topic that we will not get to until Monday's lecture. So if you prefer to wait and turn that in with the next homework, that is ok. Sorry for the late notice.
(9/5) We have set up an on-line question-and-answer system using
, which we encourage you to use to post questions and engage in discussions.
(9/5) Office hours are cancelled today, due to prelims.
(8/29) Welcome to Ma221!
Course Overview in
, including syllabus, prerequisites, pointers to other references, and grading.
. Please fill this out and email it to email@example.com if you did not get the copy in class.
An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
, is a very easy to understand description of one of the most popular iterative methods for solving A*x=b. In contrast to the terse treatment in the course text book, you might want to see Shewchuk's answer to the question "How could fifteen lines of code take fifty pages to explain?"
Lectures notes on Multigrid, in
Applied Numerical Linear Algebra
by J. Demmel, published by
List of Errata for the Textbook
(This will be updated during the semester. Suggestions welcome!)
Matlab Programs for Homework Assignments
Other Online Software and Documentation
Matlab documentation is available from several sources, most notably by typing ``help'' into the Matlab command window.
, a repository of numerical software and related documentation
Netlib Search Facility
, a way to search for the software on Netlib that you need
GAMS - Guide to Available Math Software
, another search facility to find numerical software
Linear Algebra Software Libraries and Collections
, state-of-the-art software for dense numerical linear algebra on workstations and shared-memory parallel computers. Written in Fortran.
, a C interface to LAPACK.
, a partial version of LAPACK for distributed-memory parallel computers.
are precursors of LAPACK, dealing with linear systems and eigenvalue problems, respectively.
is a fast implementations of sparse Gaussian elimination for sequential and parallel computers, respectively.
of sparse direct linear equation solvers, by
(Berkeley Benchmarking and Optimization) is a source for automatic generation of high performance numerical codes, including
, a system for producing fast implementations of sparse-matrix-vector-multiplication. (OSKI stands for Optimized Sparse Kernel Interface, and only coincidentally is also the name of the Cal Bear mascot :) ).
Sources of test matrices for sparse matrix algorithms
University of Florida Sparse Matrix Collection
Templates for the solution of linear systems
, a collection of iterative methods, with advice on which ones to use. The web site includes on-line versions of the book (in
) as well as software.
Templates for the Solution of Algebraic Eigenvalue Problems
is a survey of algorithms and software for solving eigenvalue problems. The web site points to an html version of the book, as well as software.
is a repository for information and software for Multigrid and Domain Decomposition methods, which are widely used methods for solving linear systems arising from PDEs.
Resources for Parallel and High Performance Computing
(National Energy Research Scientific Computing Center), a DOE supercomputer center at neighboring
(Lawrence Berkeley National Lab), that provides supercomputer resources to problems of interest to DOE
provides access to the network of high performance computing facilities operated by
CS 267, Applications of Parallel Computers
, including slides and videos of lectures on parallel linear algebra
ParLab Parallelism 3-Day Short Course (2014)
, including slides and videos of (shorter) lectures on parallel linear algebra
Previous versions available
ACTS (Advanced CompuTational Software)
is a set of software tools that make it easier for programmers to write high performance scientific applications for parallel computers.
PETSc: Portable, Extensible, Toolkit for Scientific Computation
Issues related to Computer Arithmetic and Error Analysis
``Accurate and efficient expression evaluation and linear algebra,''
, J. Demmel, I. Dumitriu, O. Holtz, P. Koev Acta Numerica, V. 17, May2008
``Computing the Singular Value Decomposition with High Relative Accuracy,''
J. Demmel, M. Gu, S. Eisenstat, I. Slapnicar, K. Veselic, Z. Drmac, Lin. Alg. Appl., v 299, Nov 1999
Efficient software for very high precision floating point arithmetic
Efficient software for high precision and reproducible Basic Linear Algebra Subroutines (BLAS)
Notes on IEEE Floating Point Arithmetic,
Prof. W. Kahan
Other notes on arithmetic, error analysis, etc.
Prof. W. Kahan
Report on arithmetic error that cause the Ariane 5 Rocket Crash
The IEEE floating point standard was updated in 2008. Look
for a summary.
For a variety of papers on solving linear algebra problems with guaranteed accuracy, see
Siegfried Rump's web site