Computational Methods for General Sparse Matrices

by Zahari Zlatev

Overview

'Et moi, ...- si j'avait su comment en revenir, One service mathematics has rendered the je n 'y serais point aile.' human race. It has put common sense back where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell 0. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com- puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'elre of this series.

Product Details

ISBN-13:	9780792311546
Publisher:	Springer Netherlands
Publication date:	09/30/1991
Series:	Mathematics and Its Applications , #65
Edition description:	1991
Pages:	328
Product dimensions:	8.27(w) x 11.69(h) x 0.24(d)

Table of Contents

1. Exploiting Sparsity.- 2. Storage Schemes.- 3. General Scheme for Linear Algebraic Problems.- 4. Pivotal Strategies for Gaussian Elimination.- 5. Use of Iterative Refinement in the GE Process.- 6. Implementation of the Algorithms.- 7. Solving Least Squares Problems by Augmentation.- 8. Sparse Matrix Technique for Ordinary Differential Equations.- 9. Condition Number Estimators in a Sparse Matrix Software.- 10. Parallel Direct Solvers.- 11 Parallel Orthomin for General Sparse Matrices.- 12. Orthogonalization Methods.- 13. Two Storage Schemes for Givens Plane Rotations.- 14. Pivotal Strategies for Givens Plane Rotations.- 15. Iterative Refinement after the Plane Rotations.- 16. Preconditioned Conjugate Gradients for Givens Plane Rotations.- References.- Author Index.