Parallel Efficiency Of The Lanczos Method For Eigenvalue Problems
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Parallel Efficiency Of The Lanczos Method For Eigenvalue Problems
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Author :
language : en
Publisher:
Release Date : 1998
Parallel Efficiency Of The Lanczos Method For Eigenvalue Problems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
A Parallel Lanczos Method For Symmetric Generalized Eigenvalue Problems
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Author :
language : en
Publisher:
Release Date : 1997
A Parallel Lanczos Method For Symmetric Generalized Eigenvalue Problems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
Lanczos algorithm is a very effective method for finding extreme eigenvalues of symmetric matrices. It requires less arithmetic operations than similar algorithms, such as, the Arnoldi method. In this paper, the authors present their parallel version of the Lanczos method for symmetric generalized eigenvalue problem, PLANSO. PLANSO is based on a sequential package called LANSO which implements the Lanczos algorithm with partial re-orthogonalization. It is portable to all parallel machines that support MPI and easy to interface with most parallel computing packages. Through numerical experiments, they demonstrate that it achieves similar parallel efficiency as PARPACK, but uses considerably less time.
Parallel Efficiency Of Lanczos Arnoldi And Jacobi Davidson Type Methods On Large Scale Standard Eigenvalue Problem
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Author : 王聖毅
language : en
Publisher:
Release Date : 2012
Parallel Efficiency Of Lanczos Arnoldi And Jacobi Davidson Type Methods On Large Scale Standard Eigenvalue Problem written by 王聖毅 and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
A Lanczos Eigenvalue Method On A Parallel Computer
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Author :
language : en
Publisher:
Release Date : 1987
A Lanczos Eigenvalue Method On A Parallel Computer written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
Large Scale Eigenvalue Problems
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Author : J. Cullum
language : en
Publisher: Elsevier
Release Date : 1986-01-01
Large Scale Eigenvalue Problems written by J. Cullum and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-01-01 with Mathematics categories.
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.
The Use Of Lanczos S Method To Solve The Large Generalized Symmetric Definite Eigenvalue Problem
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Author : Institute for Computer Applications in Science and Engineering
language : en
Publisher:
Release Date : 1989
The Use Of Lanczos S Method To Solve The Large Generalized Symmetric Definite Eigenvalue Problem written by Institute for Computer Applications in Science and Engineering and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.
The generalized eigenvalue problem, Kx = lambda Mx, is of significant practical importance, especially in structural engineering where it arises as the vibration and buckling problems. A new algorithm, LANZ, based on Lanczos's method is developed. LANZ uses a technique called dynamic shifting to improve the efficiency and reliability of the Lanczos algorithm. A new algorithm for solving the tridiagonal matrices that arise when using Lanczos's method is described. A modification of Parlett and Scott's selective orthogonalization algorithm is proposed. Results from an implementation of LANZ on a Convex C-220 show it to be superior to a subspace iteration code. (KR).
Using Parallel Banded Linear System Solvers In Generalized Eigenvalue Problems
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Author : Hong Zhang
language : en
Publisher:
Release Date : 1993
Using Parallel Banded Linear System Solvers In Generalized Eigenvalue Problems written by Hong Zhang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Eigenvalues categories.
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."
Lanczos Eigensolution Method For High Performance Computers
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Author :
language : en
Publisher:
Release Date : 1991
Lanczos Eigensolution Method For High Performance Computers written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.
The Use Of Lanczo S Method To Solve The Large Generalized Symmetric Eigenvalue Problem In Parallel
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Author : Institute for Computer Applications in Science and Engineering
language : en
Publisher:
Release Date : 1990
The Use Of Lanczo S Method To Solve The Large Generalized Symmetric Eigenvalue Problem In Parallel written by Institute for Computer Applications in Science and Engineering and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.
The generalized eigenvalue problem, Kx=LamdaMx, is of significant practical importance, especially in structural engineering where it arises as the vibration and buckling problems. New software, LANZ, based on Lanczo's method has been developed for solving these problems and uns on SUN 3, SUN 4, Convex C-220, Cray 2, and Cray Y-MP systems. Preliminary results of using the Force to obtain a multiprocessor implementation of LANZ on MIMD parallel/vector systems are reported here. A parallel execution time model of LANZ is defined and used to predict the performance of LANZ as well as examine hypothetical modifications to LANZ. The results of using dynamic shifting to improve parallelism are presented. Finally, the results of assigning a group of processors to separate shifts and finding all the desired eigenvalues using LANZ in parallel are reported. Keywords: Eigenvalues; Parallel orientation; Mathematical methods; Computer software; Computer systems. (cp).
Parallelism In Matrix Computations
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Author : Efstratios Gallopoulos
language : en
Publisher: Springer
Release Date : 2015-07-25
Parallelism In Matrix Computations written by Efstratios Gallopoulos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-25 with Technology & Engineering categories.
This book is primarily intended as a research monograph that could also be used in graduate courses for the design of parallel algorithms in matrix computations. It assumes general but not extensive knowledge of numerical linear algebra, parallel architectures, and parallel programming paradigms. The book consists of four parts: (I) Basics; (II) Dense and Special Matrix Computations; (III) Sparse Matrix Computations; and (IV) Matrix functions and characteristics. Part I deals with parallel programming paradigms and fundamental kernels, including reordering schemes for sparse matrices. Part II is devoted to dense matrix computations such as parallel algorithms for solving linear systems, linear least squares, the symmetric algebraic eigenvalue problem, and the singular-value decomposition. It also deals with the development of parallel algorithms for special linear systems such as banded ,Vandermonde ,Toeplitz ,and block Toeplitz systems. Part III addresses sparse matrix computations: (a) the development of parallel iterative linear system solvers with emphasis on scalable preconditioners, (b) parallel schemes for obtaining a few of the extreme eigenpairs or those contained in a given interval in the spectrum of a standard or generalized symmetric eigenvalue problem, and (c) parallel methods for computing a few of the extreme singular triplets. Part IV focuses on the development of parallel algorithms for matrix functions and special characteristics such as the matrix pseudospectrum and the determinant. The book also reviews the theoretical and practical background necessary when designing these algorithms and includes an extensive bibliography that will be useful to researchers and students alike. The book brings together many existing algorithms for the fundamental matrix computations that have a proven track record of efficient implementation in terms of data locality and data transfer on state-of-the-art systems, as well as several algorithms that are presented for the first time, focusing on the opportunities for parallelism and algorithm robustness.