Textbooks
There is no required text for the course,
but the three books below are recommended.
All three are published by SIAM,
the Society for Industrial and Applied Mathematics.
UCSB students can sign up for
free
student membership in SIAM,
which gives you a big discount on their book prices (and is a good
idea for lots of other reasons too).
- J. Demmel,
Applied
Numerical Linear Algebra. SIAM, 1997.
(This is a wonderful book and you should buy it if you plan
to do anything in computational science or numerical analysis.
It has an excellent chapter on conjugate gradients, but not
much on preconditioning.)
- Y. Saad,
Iterative
Methods for Linear Systems. SIAM, second edition 2003.
(The first edition is available
online
without charge. Both editions have a comprehensive background on
iterative methods, and are especially strong on incomplete
factorization preconditioning for nonsymmetric problems.)
- R. Barrett and 9 other authors,
Templates
for the Solution of Linear Systems:
Building Blocks for Iterative Methods. SIAM, 1994.
(The full text is also available online in
postscript and
html
without charge.
This contains very concise but very useful descriptions of many
iterative methods, with a little on preconditioning.)
Papers (this list will grow during the quarter)
- Michele Benzi's
survey of preconditioning.
(We'll read most of this in the first several weeks of class.)
- J. Shewchuk,
An introduction to the conjugate gradient
method without the agonizing pain. (What it says. A good paper.)
- Several papers on support graph preconditioning:
- Doron Chen and Sivan Toledo,
Vaidya's
preconditioners: Implementation and experimental study.
(The best available experimental work on support-graph preconditioners.)
- Erik Boman and Bruce Hendrickson,
Support
theory for preconditioning.
(A good exposition of the theory behind support-graph preconditioners,
only slightly out of date.)
- Marshall Bern et al.,
Support-graph preconditioners.
(This contains the proof of the bounds for MILU on the model problem
in two and three dimensions. Other than that, it's better to read
Boman and Hendrickson for the theory.)
- Dan Spielman and Shang-Hua Teng,
Nearly-linear time
algorithms for graph partitioning, graph sparsification, and
solving linear systems.
(The most elaborate work on support theory so far, very theoretical
but very pretty. Teasing a practically useful algorithm out of this
work may or may not be possible.)
- Barry Smith, Petter Bjorstad, and William Gropp,
Domain Decomposition:
Parallel Multilevel Methods for Elliptic Partial Differential
Equations.
(A comprehensive book on various domain decomposition
methods and multigrid.)