Sparse Matrices and their Applications

1. Front Matter

   Pages i-xii

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2. Introduction

   1. Front Matter

      Pages 1-1

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   2. Symposium on Sparse Matrices and Their Applications

      • Donald J. Rose, Ralph A. Willoughby

      Pages 3-22

3. Computational Circuit Design

   1. Front Matter

      Pages 23-23

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   2. Eigenvalue Methods for Sparse Matrices

      • D. A. Calahan, W. J. McCalla

      Pages 25-30

   3. Sparse Matrix Approach to the Frequency Domain Analysis of Linear Passive Electrical Networks

      • Albert M. Erisman

      Pages 31-40

   4. Some Basic Techniques for Solving Sparse Systems of Linear Equations

      • Fred G. Gustavson

      Pages 41-52

   5. Vector and Matrix Variability Type in Sparse Matrix Algorithms

      • Gary D. Hachtel

      Pages 53-64

4. Linear Programming

   1. Front Matter

      Pages 65-65

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   2. The Partitioned Preassigned Pivot Procedure (P4)

      • Eli Hellerman, Dennis C. Rarick

      Pages 67-76

   3. Modifying Triangular Factors of the Basis in the Simplex Method

      • John A. Tomlin

      Pages 77-85

5. Partial Differential Equations

   1. Front Matter

      Pages 87-87

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   2. A New Iterative Procedure for the Solution of Sparse Systems of Linear Difference Equations

      • David J. Evans

      Pages 89-100

   3. Block Elimination on Finite Element Systems of Equations

      • J. Alan George

      Pages 101-114

   4. Application of the Finite Element Method to Regional Water Transport Phenomena

      • G. L. Guymon, I. P. King

      Pages 115-120

   5. On the use of Fast Methods for Separable Finite Difference Equations for the Solution of General Elliptic Problems

      • Olof B. Widlund

      Pages 121-131

6. Special Topics

   1. Front Matter

      Pages 133-133

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   2. Application of Sparse Matrices to Analytical Photogrammetry

      • Gary H. Glaser, Michael S. Saliba

      Pages 135-146

   3. Generalized view of a Data Base

      • Gerhard E. Hoernes

      Pages 147-154

7. Combinatorics and Graph Theory

   1. Front Matter

      Pages 155-155

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This book contains papers on sparse matrices and their appli­ cations which were presented at a Symposium held at the IBM Thomas J. Watson Research Center, Yorktown Heights, New York on September 9-10, 1971. This is a very active field of research since efficient techniques for handling sparse matrix calculations are an important aspect of problem solving. In large scale problems, the feasibility of the calculation depends critically on the efficiency of the underlying sparse matrix algorithms. An important feature of the conference and its proceedings is the cross-fertilization achieved among a broad spectrum of application areas, and among combinatorialists, numerical analysts, and computer scientists. The mathematical, programming, and data management features of these techniques provide a unifying theme which can benefit readers in many fields. The introduction summarizes the major ideas in each paper. These ideas are interspersed with a brief survey of sparse matrix technology. An extensive unified bibliography is provided for the reader interested in more systematic information. The editors wish to thank Robert K. Brayton for his many helpful suggestions as chairman of the organizing committee and Redmond O'Brien for his editorial and audio-visual assistance. We would also like to thank Mrs. Tiyo Asai and Mrs. Joyce Otis for their help during the conference and on the numerous typing jobs for the manuscript. A special thanks goes to William J. Turner for establishing the IBM Research Symposia Series with Plenum Press.

• Mathematica
• algorithms
• computation
• efficiency
• graph algorithm
• graph theory
• information
• linear optimization
• network
• programming

• Department of Mathematics, University of Denver, Denver, USA

  Donald J. Rose

• Mathematical Sciences Department, IBM Thomas J. Watson Research Center, Yorktown Heights, USA

  Ralph A. Willoughby

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