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| Titel: |
MONITORING THE CONVERGENCE OF THE LANCZOS ALGORITHM IN PARALLEL COMPUTING ENVIRONMENTS |
| Auteur: |
Szularz, M. Weston, J. Murphy, K. Clint, M. |
| Verschenen in: |
International journal of parallel, emergent and distributed systems |
| Paginering: | Jaargang 6 (1995) nr. 4 pagina's 287-302 |
| Jaar: |
1995 |
| Inhoud: |
The Lanczos algorithm is one of the most efficient methods for finding a small number of extreme eigenvalues and corresponding eigenvectors of large, sparse, symmetric matrices. In order to monitor its convergence the algorithm is usually supplemented with a routine which incorporates the computation of partial eigensolutions of the tridiagonal matrices generated successively by the method. In this paper a new convergence monitoring routine which avoids the computation of these partial eigensolutions is proposed. In this routine approximations to the required eigenvalues are computed at each stage, the accuracy of which increase as the Lanczos method progresses. This sequence of approximations converges onto the required eigenvalues with the added advantage that no eigensolution of the final matrix is required. The Lanczos algorithm with complete reorthogonalization and with the new convergence monitoring routine has been implemented on a shared memory Convex C3840 with two processors, and on a 16-node Intel iPSC/860 hypercube. The test results show that the new convergence monitor improves the performance of the Lanczos algorithm on a single processor substantially; that it can gainfully exploit the facilities of the shared memory machine; but does not improve significantly the performance of the Lanczos algorithm on the distributed memory machine. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
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