Research Article

Improved the Convergence of Iterative Methods for Solving Systems of Equations by Memetics Techniques

by  Liviu Octavian Mafteiu-Scai
journal cover
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 64 - Issue 17
Published: February 2013
Authors: Liviu Octavian Mafteiu-Scai
10.5120/10729-5733
PDF

Liviu Octavian Mafteiu-Scai . Improved the Convergence of Iterative Methods for Solving Systems of Equations by Memetics Techniques. International Journal of Computer Applications. 64, 17 (February 2013), 33-38. DOI=10.5120/10729-5733

                        @article{ 10.5120/10729-5733,
                        author  = { Liviu Octavian Mafteiu-Scai },
                        title   = { Improved the Convergence of Iterative Methods for Solving Systems of Equations by Memetics Techniques },
                        journal = { International Journal of Computer Applications },
                        year    = { 2013 },
                        volume  = { 64 },
                        number  = { 17 },
                        pages   = { 33-38 },
                        doi     = { 10.5120/10729-5733 },
                        publisher = { Foundation of Computer Science (FCS), NY, USA }
                        }
                        %0 Journal Article
                        %D 2013
                        %A Liviu Octavian Mafteiu-Scai
                        %T Improved the Convergence of Iterative Methods for Solving Systems of Equations by Memetics Techniques%T 
                        %J International Journal of Computer Applications
                        %V 64
                        %N 17
                        %P 33-38
                        %R 10.5120/10729-5733
                        %I Foundation of Computer Science (FCS), NY, USA
Abstract

This work proposes proposed a technique inspired by memetic algorithm (MA) to improve the convergence of iterative methods for solving systems of equations. In the first phase the system of equations is transformed into an optimization problem. In this first phase, a memetics technique -ie a double optimization, local and global- is used to determine an initial vector favorable to a rapid convergence. In the second phase the system of equations is solved using an iterative method with the initial vector obtained in the previous phase. One can say that it is a hybrid method of solving systems of equations, both linear and nonlinear. The experimental results obtained with conjugate gradient, preconditioned conjugate gradient, Newton, Chebyshev and Broyden methods, serial and parallel versions, recommend the proposed method.

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Index Terms
Computer Science
Information Sciences
No index terms available.
Keywords

systems of equations memetic algorithms iterative methods convergence intial vector basin of attraction

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