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Algorithms 2015, 8(3), 774-785; doi:10.3390/a8030774

Parallel Variants of Broyden’s Method

West University of Timisoara, B-dul V. Parvan No.4, Timisoara 300223, Romania
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Academic Editors: Alicia Cordero, Juan R. Torregrosa and Francisco I. Chicharro
Received: 23 June 2015 / Revised: 27 August 2015 / Accepted: 1 September 2015 / Published: 15 September 2015
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems)
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Abstract

In this paper we investigate some parallel variants of Broyden’s method and, for the basic variant, we present its convergence properties. The main result is that the behavior of the considered parallel Broyden’s variants is comparable with the classical parallel Newton method, and significantly better than the parallel Cimmino method, both for linear and nonlinear cases. The considered variants are also compared with two more recently proposed parallel Broyden’s method. Some numerical experiments are presented to illustrate the advantages and limits of the proposed algorithms. View Full-Text
Keywords: systems of equations; Broyden’s method; parallel algorithms systems of equations; Broyden’s method; parallel algorithms
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Bistran, I.; Maruster, S.; Mafteiu-Scai, L.O. Parallel Variants of Broyden’s Method. Algorithms 2015, 8, 774-785.

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