# U.C. Berkeley Math 221 Home Page

## Matrix Computations / Numerical Linear Algebra

*Fall 2014*

MWF 11-12, 2 Evans Hall

### Instructor:

### Reader:

The reader for Ma221 is Nick Knight
(send email)
###
Administrative Assistants:

Roxana Infante / Tammy Johnson
Offices: 563 / 565 Soda Hall
Phones: (510)643-1455 / (510)643-4816
Email: (to Roxana) /
(to Tammy)
### Announcements:

(11/2) The due date for Homework 9 is extended until Nov 5.
(10/29) I posted an updated version of
Lecture 22 at 9am today.
(10/23) Answers for HW 5, 6 and 7 are posted at
bcourses.berkeley.edu.
(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
bcourses.berkeley.edu.
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
Piazza, 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!
###
Handouts

Course Overview in
pdf,
including syllabus, prerequisites, pointers to other references, and grading.
Class Survey
.
Please fill this out and email it to demmel@berkeley.edu if you did
not get the copy in class.
An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
by Jonathan Shewchuk,
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
powerpoint.
###
Textbook

*Applied Numerical Linear Algebra* by J. Demmel, published by
SIAM, 1997.
List of Errata for the Textbook
(This will be updated during the semester. Suggestions welcome!)
###
Other Online Software and Documentation

Matlab documentation is available from several sources, most notably
by typing ``help'' into the Matlab command window.
Netlib, 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
LAPACK, state-of-the-art software for dense numerical linear algebra on
workstations and shared-memory parallel computers. Written in Fortran.
LAPACK Manual
LAPACKE, a C interface to LAPACK.
ScaLAPACK, a partial version of LAPACK for distributed-memory parallel computers.
ScaLAPACK manual
LINPACK and
EISPACK are precursors of
LAPACK, dealing with linear systems and eigenvalue problems, respectively.
SuperLU
is a fast implementations of sparse Gaussian elimination for
sequential and parallel computers, respectively.
Updated survey
of sparse direct linear equation solvers, by
Xiaoye Li
BEBOP (Berkeley Benchmarking and
Optimization) is a source for automatic generation of high performance
numerical codes, including OSKI,
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
Matrix Market
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 html
and postscript)
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.
MGNet 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
NERSC (National Energy Research Scientific Computing Center),
a DOE supercomputer center at neighboring
LBL (Lawrence Berkeley National Lab), that provides
supercomputer resources to problems of interest to DOE
XSEDE provides access to the
network of high performance computing facilities operated by
NSF
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 here
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
ARPREC
GMP
Efficient software for high precision and reproducible Basic Linear Algebra Subroutines (BLAS)
XBLAS
ReproBLAS
Notes on IEEE Floating Point Arithmetic, by
Prof. W. Kahan
Other notes on arithmetic, error analysis, etc. by
Prof. W. Kahan
Report on arithmetic error that cause the Ariane 5 Rocket Crash
The IEEE floating point standard was updated in 2008.
Look here
for a summary.
For a variety of papers on solving linear algebra problems with
guaranteed accuracy, see Siegfried Rump's web site