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 million in 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 in the 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 of the
authors and colleagues. This includes a discussion of techniques for exploiting parallel architectures and new work for indefinite and unsymmetric systems.
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 million in 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 in the 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 of the
authors and colleagues. This includes a discussion of techniques for exploiting parallel architectures and new work for indefinite and unsymmetric systems.
1: Introduction
2: Sparse matrices: storage schemes and simple operations
3: Gaussian elimination for dense matrices: the algebraic
problem
4: Gaussian elimination for dense matrices: numerical
considerations
5: Gaussian elimination for sparse matrices: an introduction
6: Reduction to block triangular form
7: Local pivotal strategies for sparse matrices
8: Ordering sparse matrices for band solution
9: Orderings based on dissection
10: Implementing Gaussian elimination without symbolic
factorize
11: Implementing Gaussian elimination with symbolic factorize
12: Gaussian elimination using trees
13: Graphs for symmetric and unsymmetric matrices
14: The SOLVE phase
15: Other sparsity-oriented issues
A: Matrix and vector norms
B: Pictures of sparse matrices
C: Solutions to selected exercises
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.
J. K. (John) Reid is an Honorary Scientist at the STFC Rutherford
Appleton Laboratory in Oxfordshire, England. He is also a Visiting
Professor at the Shrivenham Campus of Cranfield University and is
Convener of the ISO/IEC Fortran Committee.
A. M. (Al) Erisman is the Executive in Residence in the School of
Business, Government, and Economics at Seattle Pacific University
and is executive editor of Ethix magazine (), which he co-founded
with a colleague in 1998. Over the past 15 years he has lectured on
five continents in areas of business, technology, mathematics,
ethics, faith, and economic development.
`Review from previous edition `an outstanding contribution to the
literature on sparse matrices...a valuable addition to the
bookshelf of every reader interested in the solution of large
sparse problems.''
SIAM Review
`'... strongly recommended to everyone involved in the study of
sparsity problems as well as those who have to solve their own
problems which need the use of sparse techniques.''
Automatica
`'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 für Mathematik
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