Open AccessJournal Article
A parallel block Lanczos algorithm and its implementation for the evaluation of some eigenvalues of large sparse symmetric matrices on multicomputers
TL;DR: HPEC (High Performance Eigenvalues Computation), a parallel software package for the evaluation of some eigenvalues of a large sparse symmetric matrix, implements an efficient and portable Block Lanczos algorithm for distributed memory multicomputers.
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Abstract: In the present work we describe HPEC (High Performance Eigenvalues Computation), a parallel software package for the evaluation of some eigenvalues of a large sparse symmetric matrix. It implements an efficient and portable Block Lanczos algorithm for distributed memory multicomputers. HPEC is based on basic linear algebra operations for sparse and dense matrices, some of which have been derived by ScaLAPACK library modules. Numerical experiments have been carried out to evaluate HPEC performance on a cluster of workstations with test matrices from Matrix Market and Higham’s collections. A comparison with a PARPACK routine is also detailed. Finally, parallel performance is evaluated on random matrices, using standard parameters.
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References
An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
TL;DR: In this article, a systematic method for finding the latent roots and principal axes of a matrix, without reducing the order of the matrix, has been proposed, which is characterized by a wide field of applicability and great accuracy, since the accumulation of rounding errors is avoided, through the process of minimized iterations.
ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods
Richard B. Lehoucq,Danny C. Sorensen,C. Yang +2 more
- 01 Jan 1998
TL;DR: The Arnoldi factorization, the implicitly restarted Arnoldi method: structure of the Eigenvalue problem Krylov subspaces and projection methods, and more.
3.3K
A set of level 3 basic linear algebra subprograms
TL;DR: This paper describes an extension to the set of Basic Linear Algebra Subprograms targeted at matrix-vector operations that should provide for efficient and portable implementations of algorithms for high-performance computers.
•Book
Lanczos algorithms for large symmetric eigenvalue computations
Jane Cullum,Ralph A. Willoughby +1 more
- 01 Jan 1985
TL;DR: This chapter discusses Lanczos Procedures with no Reorthogonalization for Real Symmetric Problems, and an Identification Test, 'Good' versus' spurious' Eigenvalues.
1.5K