Solving Large Scale Eigenvalue Problems On Vector Parallel Processors
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Large Scale Eigenvalue Problems
| Author | : J. Cullum |
| Publisher | : Elsevier |
| Total Pages | : 339 |
| Release | : 1986-01-01 |
| Genre | : Mathematics |
| ISBN | : 0080872387 |
Results of research into large scale eigenvalue problems are presented in this volume. The papers fall into four principal categories: novel algorithms for solving large eigenvalue problems, novel computer architectures, computationally-relevant theoretical analyses, and problems where large scale eigenelement computations have provided new insight.
Vector and Parallel Processing - VECPAR'98
| Author | : Jose M.L.M. Palma |
| Publisher | : Springer |
| Total Pages | : 721 |
| Release | : 2006-10-11 |
| Genre | : Computers |
| ISBN | : 3540485163 |
This book constitutes the thoroughly refereed post-conference proceedings of the Third International Conference on Vector and Parallel Processing, VECPAR'98, held in Porto, Portugal, in June 1998. The 41 revised full papers presented were carefully selected during two rounds of reviewing and revision. Also included are six invited papers and introductory chapter surveys. The papers are organized in sections on eigenvalue problems and solutions of linear systems; computational fluid dynamics, structural analysis, and mesh partitioning; computing in education; computer organization, programming and benchmarking; image analysis and synthesis; parallel database servers; and nonlinear problems.
Numerical Linear Algebra for High-performance Computers
| Author | : Jack J. Dongarra |
| Publisher | : SIAM |
| Total Pages | : 360 |
| Release | : 1998-01-01 |
| Genre | : Computers |
| ISBN | : 9780898719611 |
This book presents a unified treatment of recently developed techniques and current understanding about solving systems of linear equations and large scale eigenvalue problems on high-performance computers. It provides a rapid introduction to the world of vector and parallel processing for these linear algebra applications. Topics include major elements of advanced-architecture computers and their performance, recent algorithmic development, and software for direct solution of dense matrix problems, direct solution of sparse systems of equations, iterative solution of sparse systems of equations, and solution of large sparse eigenvalue problems.
Numerical Methods for Large Eigenvalue Problems
| Author | : Yousef Saad |
| Publisher | : SIAM |
| Total Pages | : 292 |
| Release | : 2011-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781611970739 |
This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.
Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing
| Author | : Tetsuya Sakurai |
| Publisher | : Springer |
| Total Pages | : 312 |
| Release | : 2018-01-03 |
| Genre | : Computers |
| ISBN | : 3319624261 |
This book provides state-of-the-art and interdisciplinary topics on solving matrix eigenvalue problems, particularly by using recent petascale and upcoming post-petascale supercomputers. It gathers selected topics presented at the International Workshops on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2014 and EPASA2015), which brought together leading researchers working on the numerical solution of matrix eigenvalue problems to discuss and exchange ideas – and in so doing helped to create a community for researchers in eigenvalue problems. The topics presented in the book, including novel numerical algorithms, high-performance implementation techniques, software developments and sample applications, will contribute to various fields that involve solving large-scale eigenvalue problems.
Using Parallel Banded Linear System Solvers in Generalized Eigenvalue Problems
| Author | : Hong Zhang |
| Publisher | : |
| Total Pages | : 24 |
| Release | : 1993 |
| Genre | : Eigenvalues |
| ISBN | : |
Abstract: "Subspace iteration is a reliable and cost effective method for solving positive definite banded symmetric generalized eigenproblems, especially in the case of large scale problems. This paper discusses an algorithm that makes use of two parallel banded solvers in subspace iteration. A shift is introduced to decompose the banded linear systems into relatively independent subsystems and to accelerate the iterations. With this shift, an eigenproblem is mapped efficiently into the memories of a multiprocessor and a high speed-up is obtained for parallel implementations. An optimal shift is a shift that balances total computation and communication costs. Under certain conditions, we show how to estimate an optimal shift analytically using the decay rate for the inverse of a banded matrix, and how to improve this estimate. Computational results on iPSC/2 and iPSC/860 multiprocessors are presented."
Templates for the Solution of Algebraic Eigenvalue Problems
| Author | : Zhaojun Bai |
| Publisher | : SIAM |
| Total Pages | : 439 |
| Release | : 2000-01-01 |
| Genre | : Computers |
| ISBN | : 9780898719581 |
Large-scale problems of engineering and scientific computing often require solutions of eigenvalue and related problems. This book gives a unified overview of theory, algorithms, and practical software for eigenvalue problems. It organizes this large body of material to make it accessible for the first time to the many nonexpert users who need to choose the best state-of-the-art algorithms and software for their problems. Using an informal decision tree, just enough theory is introduced to identify the relevant mathematical structure that determines the best algorithm for each problem.
Vector and Parallel Processing - VECPAR'96
| Author | : Jack Dongarra |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 494 |
| Release | : 1997-04-09 |
| Genre | : Computers |
| ISBN | : 9783540628286 |
This book constitutes a carefully arranged selection of revised full papers chosen from the presentations given at the Second International Conference on Vector and Parallel Processing - Systems and Applications, VECPAR'96, held in Porto, Portugal, in September 1996. Besides 10 invited papers by internationally leading experts, 17 papers were accepted from the submitted conference papers for inclusion in this documentation following a second round of refereeing. A broad spectrum of topics and applications for which parallelism contributes to progress is covered, among them parallel linear algebra, computational fluid dynamics, data parallelism, implementational issues, optimization, finite element computations, simulation, and visualisation.
