CS 290H, Fall 2005: References

Textbooks

I will assign readings in literature available online. 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).

• 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. The second edition, but not the first, has a chapter on multigrid.

• 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.

• 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.

Papers (this list will grow during the quarter)

• Michele Benzi's survey of preconditioning.

• J. Shewchuk, An introduction to the conjugate gradient method without the agonizing pain. (What it says. A good paper.)

• The 2005 Preconditioning Conference proceedings.

• 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 (A good exposition of the theory behind support-graph preconditioners, only slightly out of date.)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.)

• References on multigrid and domain decomposition:
• Bill Briggs, Van Henson, and Steve McCormick, A Multigrid Tutorial, published by SIAM. (A superb tutorial. The text isn't online but this home page includes an excellent set of slides that follows the book.)
• MGNet home page. (A repository of all sorts of multigrid software, tutorials, papers, and information.)
• 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.)

Software

• LDL, an example due to Tim Davis of a mexFunction that interfaces a C code to Matlab.

• The mesh partitioning toolbox, which includes utilities for generating grid graphs, analyzing elimination orders, plotting graphs and elimination trees, and nested dissection ordering. Includes a Matlab interface to the Metis partitioning and ordering software.

• TAUCS, a library of software by Sivan Toledo's group at Tel-Aviv that contains direct solvers and many different preconditioners, including several support-graph preconditioners.