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Solving Linear Systems of Equations using a Memetic Algorithm
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 58 - Number 13 |
| Year of Publication: 2012 |
| Authors: Liviu Octavian Mafteiu-Scai, Emanuela Jana Mafteiu-Scai |
10.5120/9341-3658
|
Liviu Octavian Mafteiu-Scai, Emanuela Jana Mafteiu-Scai . Solving Linear Systems of Equations using a Memetic Algorithm. International Journal of Computer Applications. 58, 13 ( November 2012), 16-22. DOI=10.5120/9341-3658
Abstract
This paper proposes a memetic algorithm (MA) to solve linear systems of equations, by transforming the linear system of equations into an optimization problem. Such exploitation of knowledge obtained in a local search/optimization allows the evolutionary programming implementation to produce very good results at a relatively low computational cost. The proposed MA is able to determine solutions of a given linear system of equations, even in cases where traditional methods fail (determinant null, ill-conditioned systems, subdeterminate systems, supradeterminate systems, system doesn't satisfy the convergence conditions etc). In situations when a linear system of equations has multiple solutions, in proposed approach, the task is to find as many solutions as possible,inside of a given interval. In cases where no accurate solution for a linear system of equations exists, an approximate solution can be acceptable and it can be obtained by the proposed method.
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