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Contributors

Preface

I. Design and Analysis of Elimination Algorithms

1. Graph Theory and Gaussian Elimination

2. Partitioning Using PAQ

3. Block Methods for Solving Sparse Linear Systems

4. A Recursive Analysis of Dissection Strategies

5. Applications of an Element Model for Gaussian Elimination

6. An Optimization Problem Arising from Tearing Methods

II. Eigenvalue Problems

1. A Bibliographical Tour of the Large, Sparse Generalized Eigenvalue Problem

2. How Far Should You Go With the Lanczos Process?

III. Optimization, Least Squares and Linear Programming

1. Optimization for Sparse Systems

2. Methods for Sparse Linear Least Squares Problems

3. The Orthogonal Factorization of a Large Sparse Matrix

4. A Fast, Stable Implementation of the Simplex Method Using Bartels-Golub Updating

5. Using the Steepest-Edge Simplex Algorithm to Solve Sparse Linear Programs

IV. Mathematical Software

1. Sparse Matrix Software

2. Considerations in the Design of Software for Sparse Gaussian Elimination

3. Finding the Block Lower Triangular Form of a Sparse Matrix

V. Matrix Methods for Partial Difference Equations

1. Marching Algorithms and Block Gaussian Elimination

2. A Generalized Conjugate Gradient Method for the Numerical Solution of Elliptic Partial Differential Equations

3. Preconditioned Conjugate Gradient Iteration Applied to Galerkin Methods for a Mildly-Nonlinear Dirichlet Problem

4. The Sparse Tableau Approach to Finite Element Assembly

5. A Capacitance Matrix Technique

6. M-Matrix Theory and Recent Results in Numerical Linear Algebra

VI. Applications

1. Sparse Matrix Problems in a Finite Element Open Ocean Model

2. Calculation of Normal Modes of Oceans Using a Lanczos Method

3. Application of Sparse Matrix Techniques to Reservoir Simulation

4. On the Origins and Numerical Solution of Some Sparse Nonlinear Systems

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1st Edition - January 1, 1976

Editors: James R. Bunch, Donald J. Rose

Language: EnglisheBook ISBN:

9 7 8 - 1 - 4 8 3 2 - 6 3 4 0 - 3

Sparse Matrix Computations is a collection of papers presented at the 1975 Symposium by the same title, held at Argonne National Laboratory. This book is composed of six parts… Read more

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Sparse Matrix Computations is a collection of papers presented at the 1975 Symposium by the same title, held at Argonne National Laboratory. This book is composed of six parts encompassing 27 chapters that contain contributions in several areas of matrix computations and some of the most potential research in numerical linear algebra. The papers are organized into general categories that deal, respectively, with sparse elimination, sparse eigenvalue calculations, optimization, mathematical software for sparse matrix computations, partial differential equations, and applications involving sparse matrix technology. This text presents research on applied numerical analysis but with considerable influence from computer science. In particular, most of the papers deal with the design, analysis, implementation, and application of computer algorithms. Such an emphasis includes the establishment of space and time complexity bounds and to understand the algorithms and the computing environment. This book will prove useful to mathematicians and computer scientists.

Contributors

Preface

I. Design and Analysis of Elimination Algorithms

1. Graph Theory and Gaussian Elimination

2. Partitioning Using PAQ

3. Block Methods for Solving Sparse Linear Systems

4. A Recursive Analysis of Dissection Strategies

5. Applications of an Element Model for Gaussian Elimination

6. An Optimization Problem Arising from Tearing Methods

II. Eigenvalue Problems

1. A Bibliographical Tour of the Large, Sparse Generalized Eigenvalue Problem

2. How Far Should You Go With the Lanczos Process?

III. Optimization, Least Squares and Linear Programming

1. Optimization for Sparse Systems

2. Methods for Sparse Linear Least Squares Problems

3. The Orthogonal Factorization of a Large Sparse Matrix

4. A Fast, Stable Implementation of the Simplex Method Using Bartels-Golub Updating

5. Using the Steepest-Edge Simplex Algorithm to Solve Sparse Linear Programs

IV. Mathematical Software

1. Sparse Matrix Software

2. Considerations in the Design of Software for Sparse Gaussian Elimination

3. Finding the Block Lower Triangular Form of a Sparse Matrix

V. Matrix Methods for Partial Difference Equations

1. Marching Algorithms and Block Gaussian Elimination

2. A Generalized Conjugate Gradient Method for the Numerical Solution of Elliptic Partial Differential Equations

3. Preconditioned Conjugate Gradient Iteration Applied to Galerkin Methods for a Mildly-Nonlinear Dirichlet Problem

4. The Sparse Tableau Approach to Finite Element Assembly

5. A Capacitance Matrix Technique

6. M-Matrix Theory and Recent Results in Numerical Linear Algebra

VI. Applications

1. Sparse Matrix Problems in a Finite Element Open Ocean Model

2. Calculation of Normal Modes of Oceans Using a Lanczos Method

3. Application of Sparse Matrix Techniques to Reservoir Simulation

4. On the Origins and Numerical Solution of Some Sparse Nonlinear Systems

- No. of pages: 468
- Language: English
- Edition: 1
- Published: January 1, 1976
- Imprint: Academic Press
- eBook ISBN: 9781483263403

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