Parallel and systolic solution of normalized explicit approximate inverse preconditioning

Authors:
G. A. Gravvanis;K. M. Giannoutakis;M. P. Bekakos;O. B. Efremides
Affiliations:
Department of Computer Science, Hellenic Open University, Patras, Hellas;Department of Informatics and Telecommunications, University of Athens, Panepistimiopolis, Athens, Hellas;Department of Electrical & Computer Engineering, School of Engineering, Democritus University of Thrace, Hellas;Department of Electrical & Computer Engineering, School of Engineering, Democritus University of Thrace, Hellas
Venue:
The Journal of Supercomputing - Special issue: Parallel and distributed processing and applications
Year:
2004

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Abstract

A new class of normalized approximate inverse matrix techniques, based on the concept of sparse normalized approximate factorization procedures are introduced for solving sparse linear systems derived from the finite difference discretization of partial differential equations. Normalized explicit preconditioned conjugate gradient type methods in conjunction with normalized approximate inverse matrix techniques are presented for the efficient solution of sparse linear systems. Theoretical results on the rate of convergence of the normalized explicit preconditioned conjugate gradient scheme and estimates of the required computational work are presented. Application of the new proposed methods on two dimensional initial/boundary value problems is discussed and numerical results are given. The parallel and systolic implementation of the dominant computational part is also investigated.