Solving systems of nonlinear equations via conjugate direction flower pollination algorithm

Rushdy, Ehab; Baset, Mohamed Abdel; Hezam, Ibrahim M.

doi:10.1504/ijcsm.2017.085732

Cited by 2 publications

(1 citation statement)

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“…Researchers have proposed many methods for solving systems of equations [1] [7] [8] (see [5] for a good discussion of these methods). These methods either solve the equations directly by applying numerical methods [4] [9][10] [11] [17] [23] or solve them indirectly by transforming the system of equations into problem optimization [2] [3][4] [5] [12] [16] [19] [22]. This paper offers a technique for solving systems of linear or nonlinear equations.…”

Section: Introductionmentioning

confidence: 99%

Probability-Directed Problem Optimization Technique for Solving Systems of Linear and Non-Linear Equations

Al-Muhammed¹

2019

Computer Science &Amp; Information Technology (CS &Amp; IT )

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Although many methods have been proposed for solving linear or nonlinear systems of equations, there is always a pressing need for more effective and efficient methods. Good methods should produce solutions with high precision and speed. This paper proposed an innovative method for solving systems of linear and nonlinear equations. This method transforms the problem into an optimization problem and uses a probability guided search technique for solving this optimization problem, which is the solution for the system of equations. The transformation results in an aggregate violation function and a criterion function. The aggregation violation function is composed of the constraints that represent the equations and whose satisfaction is a solution for the system of equations. The criterion function intelligently guides the search for the solution to the aggregate violation function by determining when the constraints must be checked; thereby avoiding unnecessary, timeintensive checks for the constraints. Experiments conducted with our prototype implementation showed that our method is effective in finding solutions with high precision and efficient in terms of CPU time.

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