Low Communication Overhead Jacobi Algorithms for Eigenvalues Computation on Hypercubes

Authors:
Dolors Royo;Antonio González;Miguel Valero-García
Affiliations:
Universitat Politècnica de Catalunya, Departament d'Arquitectura de Computadors, Jordi Girona 1-3, Mòdul D6, 08034 Barcelona, Spain, dolors@ac.upc.es;Universitat Politècnica de Catalunya, Departament d'Arquitectura de Computadors, Jordi Girona 1-3, Mòdul D6, 08034 Barcelona, Spain, antonio@ac.upc.es;Universitat Politècnica de Catalunya, Departament d'Arquitectura de Computadors, Jordi Girona 1-3, Mòdul D6, 08034 Barcelona, Spain, miguel@ac.upc.es
Venue:
The Journal of Supercomputing
Year:
1999

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Abstract

This paper presents some novel algorithms to implement the Jacobi method in hypercube multicomputers. The algorithms are based on the one-sided Jacobi method and use new Jacobi orderings, which are one of the contributions of this paper. The second contribution of this paper is the use of a systematic algorithm transformation, which is referred to as communication pipelining, and is aimed at reducing the communication overhead by exploiting parallelism in the communication operations. The proposed schemes are evaluated by means of analytical models and compared with previous proposals. The results show a significant reduction in the communication overhead, which in some cases can be by a factor almost as great as the number of dimensions of the hypercube.