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Parallel algorithms for numerical linear algebra /
This is the first in a new series of books presenting research results and developments concerning the theory and applications of parallel computers, including vector, pipeline, array, fifth/future generation computers, and neural computers.
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam ; New York :
North-Holland,
1990.
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| Colección: | Advances in parallel computing ;
v. 1. |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo |
Tabla de Contenidos:
- Front Cover; Parallel Algorithms for Numerical Linear Algebra; Copyright Page; Preface; Table of Contents; Part 1: Systolic array algorithms; Chapter 1. A quadratically convergent parallel Jacobi process for diagonally dominant matrices with distinct eigenvalues; 1. Introduction; 2. Parallel annihilators; the first step; 3. The effect of a complete sweep; 4. Numerical examples; 5. Conclusions; References; Chapter 2. A Jacobi-like algorithm for computing the generalized Schur form of a regular pencil; 1. Introduction; 2. Normal pencils; 3. Description of the method; 4. Global convergence.
- 5. Ultimate convergence6. Numerical tests; 7. Conclusion; References; Chapter 3. Canonical correlations and generalized SVD: applications and new algorithms; 1. Introduction; 2. Applications; 3. SVD of products of three matrices; 4. New algorithms; 5. Final remarks; Acknowledgements; References; Chapter 4. From Bareiss' algorithm to the stable computation of partial correlations; 1. Introduction; 2. The Generalized Bareiss algorithm; 3. Cybenko's algorithm; 4. The Hyperbolic Cholesky algorithm; 5. Application to the computation of certain sample partial correlations.
- 6. Computation of arbitrary partial correlations7. Conclusions; Acknowledgement; References; Part 2: Message-passing systems; Chapter 5. A recursive doubling algorithm for solution of tridiagonal systems on hypercube multiprocessors; 1. Introduction; 2. The LU decomposition algorithm; 3. Solution of tridiagonal systems using prefix algorithms; 4. Parallel prefix algorithms on hypercube multiprocessors; 5. Estimated speedup and efficiency; 6. Experimental results and conclusions; References; Chapter 6. Least squares modifications with inverse factorizations: parallel implications.
- 1. Introduction2. Updating R-1; 3. Downdating R-1; 4. Summary and parallel implications; Acknowledgements; References; Chapter 7. Solution of sparse positive definite systems on a hypercube; 1. Introduction; 2. Solution of sparse symmetric positive definite systems; 3. Parallel Cholesky factorization; 4. Symbolic factorization; 5. Sparse triangular solution; 6. Ordering; 7. Some experiments and concluding remarks; References; Chapter 8. Some aspects of parallel implementation of the finite-element method on message passing architectures; 1. Introduction.
- 2. The model problem and finite-element discretization3. Overview of computations; 4. Cost analysis; 5. Numerical experiments; 6. Conclusions; Appendix; References; Part 3: Algorithms for parallel shared-memory systems; Chapter 9. An overview of parallel algorithms for the singular value and symmetric eigenvalue problems; 1. Introduction; 2. Jacobi methods; 3. Reduction to tridiagonal form and multisectioning; 4. Performance of eigensolvers; 5. Singular value decomposition; 6. Performance of SVD algorithms; 7. Conclusions; Acknowledgements; References.