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Direct Methods for Sparse Linear SystemsDirect Methods for Sparse Linear Systems

Timothy A. Davis

Fundamentals of Algorithms 2

“Everything you wanted to know but never dared to ask about modern direct linear solvers.” — Chen Greif, Assistant Professor, Department of Computer Science, University of British Columbia

“Overall, the book is magnificent. It fills a long-felt need for an accessible textbook on modern sparse direct methods. Its choice of scope is excellent…” — John Gilbert, Professor, Department of Computer Science, University of California, Santa Barbara

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.

Audience This invaluable book is essential to computational scientists and software developers who want to understand the theory and algorithms behind modern techniques used to solve large sparse linear systems. The book also serves as an excellent practical resource for students with an interest in combinatorial scientific computing.

About the Author Timothy A. Davis is a 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.

Chapter 1: Introduction
Chapter 2: Basic algorithms
Chapter 3: Solving triangular systems
Chapter 4: Cholesky factorization
Chapter 5: Orthogonal methods
Chapter 6: LU factorization
Chapter 7: Fill-reducing orderings
Chapter 8: Solving sparse linear systems
Chapter 9: CSparse
Chapter 10: Sparse matrices in MATLAB
Appendix: Basics of the C programming language

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2006 / xii + 217 pages / Softcover
ISBN-13: 978-0-898716-13-9 / ISBN-10: 0-89871-613-6
List Price $72.50 / SIAM Member Price $50.75 / Order Code FA02
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Banner art adapted from a figure by Hinke M. Osinga and Bernd Krauskopf (University of Auckland, NZ.)