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

Abstract

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.