A Comparative Study on Qualification Criteria of Nonlinear Solvers with Introducing Some New Ones

Abstract

In order to compare different solvers for systems of nonlinear equations, some novel goodness and qualification criteria are defined in this paper. These use all parameters of a nonlinear solver such as convergence order, number of function evaluations, number of iterations, CPU time, etc. To achieve the criteria, different algorithms to solve nonlinear systems are categorised to three kinds. For any category, two criteria are defined to compare different algorithms in that category. As numerical results show, these new criteria can use to compare different algorithms which solve systems of nonlinear equations. Further, we present some corrected formulas for some classical efficiency indices and change them to be more applicable. Also, some suggestions are presented about the future works.