Direct Methods for Sparse Matrices

Hardcover | April 25, 2017

byI. S. Duff, A. M. Erisman, J. K. Reid

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The subject of sparse matrices has its root in such diverse fields as management science, power systems analysis, surveying, circuit theory, and structural analysis. Efficient use of sparsity is a key to solving large problems in many fields. This second edition is a complete rewrite of the first edition published 30 years ago. Much has changed since that time. Problems have grown greatly in size and complexity; nearly all examples in the first edition were of order less than 5,000 in the first edition, and are often more than a millionin the second edition. Computer architectures are now much more complex, requiring new ways of adapting algorithms to parallel environments with memory hierarchies. Because the area is such an important one to all of computational science and engineering, a huge amount of research has been done inthe last 30 years, some of it by the authors themselves. This new research is integrated into the text with a clear explanation of the underlying mathematics and algorithms.New research that is described includes new techniques for scaling and error control, new orderings, new combinatorial techniques for partitioning both symmetric and unsymmetric problems, and a detailed description of the multifrontal approach to solving systems that was pioneered by the research ofthe authors and colleagues. This includes a discussion of techniques for exploiting parallel architectures and new work for indefinite and unsymmetric systems.

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The subject of sparse matrices has its root in such diverse fields as management science, power systems analysis, surveying, circuit theory, and structural analysis. Efficient use of sparsity is a key to solving large problems in many fields. This second edition is a complete rewrite of the first edition published 30 years ago. Much h...

I. S. (Iain) Duff is an STFC Senior Fellow in the Scientific Computing Department at the STFC Rutherford Appleton Laboratory in Oxfordshire, England. He is also the Scientific Advisor for the Parallel Algorithms Group at CERFACS in Toulouse and is a Visiting Professor of Mathematics at the University of Strathclyde. A. M. (Al) Erisman ...

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Format:HardcoverDimensions:416 pages, 9.21 × 6.14 × 0.01 inPublished:April 25, 2017Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198508387

ISBN - 13:9780198508380

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Table of Contents

1. Introduction2. Sparse matrices: storage schemes and simple operations3. Gaussian elimination for dense matrices: the algebraic problem4. Gaussian elimination for dense matrices: numerical considerations5. Gaussian elimination for sparse matrices: an introduction6. Reduction to block triangular form7. Local pivotal strategies for sparse matrices8. Ordering sparse matrices for band solution9. Orderings based on dissection10. Implementing Gaussian elimination without symbolic factorize11. Implementing Gaussian elimination with symbolic factorize12. Gaussian elimination using trees13. Graphs for symmetric and unsymmetric matrices14. The SOLVE phase15. Other sparsity-oriented issuesA. Matrix and vector normsB. Pictures of sparse matricesC. Solutions to selected exercises

Editorial Reviews

"the present book makes ... digestable reading and may by its practical attitude and many methods and examples contribute to the cogent solution of linear systems." --Monatshefte fur Mathematik