Direct Methods for Sparse Linear Systems

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SIAM, Sep 1, 2006 - Computers - 217 pages
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Computational scientists often encounter problems requiring the solution of sparse systems of linear equations. Attacking these problems efficiently requires an in-depth knowledge of the underlying theory, algorithms, and data structures found in sparse matrix software libraries. Here, Davis presents the fundamentals of sparse matrix algorithms to provide the requisite background. The book includes CSparse, a concise downloadable sparse matrix package that illustrates the algorithms and theorems presented in the book and equips readers with the tools necessary to understand larger and more complex software packages. With a strong emphasis on MATLAB® and the C programming language, Direct Methods for Sparse Linear Systems equips readers with the working knowledge required to use sparse solver packages and write code to interface applications to those packages. The book also explains how MATLAB performs its sparse matrix computations.
  

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Contents

Basic algorithms
7
Solving triangular systems
27
Cholesky factorization
37
Orthogonal methods
69
LU factorization
83
Fillreducing orderings
99
Solving sparse linear systems
135
CSparse
145
Sparse matrices in MATLAB
169
A Basics of the C programming language
187
Bibliography
195
Index
211
Copyright

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Page 200 - IS DUFF. Algorithm 575: Permutations for a zero-free diagonal, ACM Trans. Math. Software, 7 (1981), pp. 387-390.
Page iv - Editorial Board Peter Benner Dianne P. O'Leary Technische Universitat Chemnitz University of Maryland John R. Gilbert Robert D. Russell University of California, Santa Barbara Simon Fraser University Michael T. Heath Robert D. Skeel University of Illinois — Urbana-Champaign Purdue University CT Kelley Danny Sorensen North Carolina State University Rice University Cleve Moler Andrew J. Wathen The MathWorks, Inc.

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About the author (2006)

Timothy A. Davis is an Associate Professor in Computer and Information Science and Engineering at the University of Florida. He is the author of a suite of sparse matrix packages that are widely used in industry, academia, and government research labs, and related articles in SIAM, ACM, and IEEE journals. He is the co-author of a well-used introduction to MATLAB, the MATLAB Primer (Chapman & Hall/CRC Press, 2005). He is a member of the editorial boards of the IEEE Transactions on Parallel and Distributed Systems, and Computational Optimization and Applications.

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