A Derivative-free Algorithm for Finding Least Squares Solutions of Quasi-linear and Linear Systems

Abstract

A novel derivative-free algorithm for solving quasilinear systems is presented. It resembles “classical” optimization approach but greatly simplifies computation, resulting in fast execution and numerical stability. Though the global convergence cannot be guaranteed, it turns out that the presented algorithm finds a solution as successfully as other commonly accepted methods. The algorithm is clearly developed and mathematically founded, and its properties are examined by comparisons with other methods.