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Parallel Algorithms for Numerical Linear Algebra.

By: Vorst, H. van der.
Contributor(s): Dooren, P. van.
Material type: TextTextSeries: eBooks on Demand.Advances in Parallel Computing: Publisher: Amsterdam : Elsevier Science, 2015Description: 1 online resource (341 p.).ISBN: 9781483295732.Subject(s): Algebras, Linear | Numerical calculations | Parallel algorithms | Parallel processing (Electronic computers)Genre/Form: Electronic books.Additional physical formats: Print version:: Parallel Algorithms for Numerical Linear AlgebraDDC classification: 004.35 Online resources: Click here to view this ebook.
Contents:
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 convergence -- 6. 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 correlations -- 7. 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. Introduction -- 2. 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 discretization -- 3. 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
Summary: 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. All aspects of high-speed computing fall within the scope of the series, e.g. algorithm design, applications, software engineering, networking, taxonomy, models and architectural trends, performance, peripheral devices. Papers in Volume One cover the main streams of parallel linear algebra: systolic array algorithms, message-passing systems, algorithms for
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Item type Current location Call number URL Status Date due Barcode
Electronic Book UT Tyler Online
Online
QA76.5 .P31458 2014 (Browse shelf) http://uttyler.eblib.com/patron/FullRecord.aspx?p=1877019 Available EBL1877019

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 convergence -- 6. 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 correlations -- 7. 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. Introduction -- 2. 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 discretization -- 3. 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

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. All aspects of high-speed computing fall within the scope of the series, e.g. algorithm design, applications, software engineering, networking, taxonomy, models and architectural trends, performance, peripheral devices. Papers in Volume One cover the main streams of parallel linear algebra: systolic array algorithms, message-passing systems, algorithms for

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