Computing Complex Roots of Systems of Nonlinear Equations Using Spiral Optimization Algorithm with Clustering

Abstract

Finding complex roots of a system of nonlinear equations is not an easy numerical computation problem. A method of locating and finding all real and complex roots of systems of nonlinear equations in a single run is proposed here. The method that was first proposed for finding all real roots of systems of nonlinear equations is now slightly modified and adapted so that it can be used also for finding complex roots of the corresponding system. The root finding problem is transformed to optimization problem and then a spiral optimization algorithm of Tamura and Yasuda is used to solve the optimization problem. In order to locate the position of the roots, we proposed a certain clustering technique. Several test problems have been examined. This combination of technique enables ones to locate and find all real and complex roots within a bounded domain in all test cases.