Parallel tridiagonalization of a general matrix using distributed-memory multiprocessors
Recently there has been a renewed interest in finding reliable methods for reducing general matrices to tridiagonal form. We have developed a serial reduction algorithm that appears to be very reliable in practice by incorporating an optimal pivot search and two recovery schemes. In this paper we describe a parallel version of our algorithm. The algorithm was developed as one step in the process of finding eigenvalues of nonsymmetric matrices. Our original parallel eigenvalue routines reduced the matrix to Hessenberg form and then applied QR iteration, but the performance of the QR iteration was disappointing. Our new parallel algorithm reduces the matrix to tridiagonal form and then applies LR iteration. Using an iPSC/2, we compare the performance of the new parallel algorithm with our previous parallel algorithm and show that the new algorithm is nearly an order of magnitude faster, allowing us to solve much larger problems than previously attempted. 13 refs., 2 figs.
- Research Organization:
- Oak Ridge National Lab., TN (USA)
- Sponsoring Organization:
- DOE/ER
- DOE Contract Number:
- AC05-84OR21400
- OSTI ID:
- 7164496
- Report Number(s):
- CONF-891273-3; ON: DE90008902
- Country of Publication:
- United States
- Language:
- English
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