Parallel Algorithms for Numerical Linear Algebra

Front Cover
 Parallel Algorithms for Numerical Linear Algebra
 Copyright Page
 Table of Contents
 Preface
 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.