Graph Theory and Sparse Matrix Computation

✍ Scribed by Jean R. S. Blair, Barry Peyton (auth.), Alan George, John R. Gilbert, Joseph W. H. Liu (eds.)

• Publisher: Springer-Verlag New York
• Year: 1993
• Tongue: English
• Leaves: 253
• Series: The IMA Volumes in Mathematics and its Applications 56
• Edition: 1
• Category: Library

✦ Synopsis

When reality is modeled by computation, matrices are often the connection between the continuous physical world and the finite algorithmic one. Usually, the more detailed the model, the bigger the matrix, the better the answer, however, efficiency demands that every possible advantage be exploited. The articles in this volume are based on recent research on sparse matrix computations. This volume looks at graph theory as it connects to linear algebra, parallel computing, data structures, geometry, and both numerical and discrete algorithms. The articles are grouped into three general categories: graph models of symmetric matrices and factorizations, graph models of algorithms on nonsymmetric matrices, and parallel sparse matrix algorithms. This book will be a resource for the researcher or advanced student of either graphs or sparse matrices; it will be useful to mathematicians, numerical analysts and theoretical computer scientists alike.

✦ Table of Contents

Front Matter....Pages i-xv
An Introduction to Chordal Graphs and Clique Trees....Pages 1-29
Cutting down on Fill Using Nested Dissection: Provably Good Elimination Orderings....Pages 31-55
Automatic Mesh Partitioning....Pages 57-84
Structural Representations of Schur Complements in Sparse Matrices....Pages 85-100
Irreducibility and Primitivity of Perron Complements: Application of the Compressed Directed Graph....Pages 101-106
Predicting Structure in Nonsymmetric Sparse Matrix Factorizations....Pages 107-139
Highly Parallel Sparse Triangular Solution....Pages 141-157
The Fan-Both Family of Column-Based Distributed Cholesky Factorization Algorithms....Pages 159-190
Scalability of Sparse Direct Solvers....Pages 191-209
Sparse Matrix Factorization on SIMD Parallel Computers....Pages 211-228
The Efficient Parallel Iterative Solution of Large Sparse Linear Systems....Pages 229-245

✦ Subjects

Combinatorics; Numerical Analysis