Chen, G. and Keller, H. B. and Lui, S. H. and Roux, B. (1992) Parallel homotopy algorithm for large sparse generalized eigenvalue problems: Application to hydrodynamic stability analysis. In: Parallel Processing: CONPAR 92—VAPP V. Lecture Notes in Computer Science. No.634. Springer , Berlin, pp. 331-342. ISBN 978-3-540-55895-8. https://resolver.caltech.edu/CaltechAUTHORS:20170802-124308426
Full text is not posted in this repository. Consult Related URLs below.
Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20170802-124308426
Abstract
A parallel homotopy algorithm is presented for finding a few selected eigenvalues (for example those with the largest real part) of Az = λBz with real, large, sparse, and nonsymmetric square matrix A and real, singular, diagonal matrix B. The essence of the homotopy method is that from the eigenpairs of Dz = λBz, we use Euler-Newton continuation to follow the eigenpairs of A(t)z = λBz with A(t) ≡ (1−t)D + tA. Here D is some initial matrix and “time” t is incremented from 0 to 1. This method is, to a large degree, parallel because each eigenpath can be computed independently of the others. The algorithm has been implemented on the Intel hypcrcubc. Experimental results on a 64-nodc Intel iPSC/860 hypercube are presented. It is shown how the parallel homotopy method may be useful in applications like detecting Hopf bifurcations in hydrodynamic stability analysis.
| Item Type: | Book Section | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Related URLs: |
| |||||||||
| Additional Information: | © 1992 Springer-Verlag. Most of the work of the author (G. C) was done during a visit to the Center for Research on Parallel Computation at Caltech with support from "Conseil Régional Provence-Alpes-Côte d'Azur (France)". All the 64-node computations have been performed on the "Gamma" machine of the Caltech Concurrent Supercomputing Facilities. | |||||||||
| Funders: |
| |||||||||
| Series Name: | Lecture Notes in Computer Science | |||||||||
| Issue or Number: | 634 | |||||||||
| DOI: | 10.1007/3-540-55895-0_427 | |||||||||
| Record Number: | CaltechAUTHORS:20170802-124308426 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170802-124308426 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 79770 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 02 Aug 2017 20:11 | |||||||||
| Last Modified: | 15 Nov 2021 17:50 |
Repository Staff Only: item control page
