Solving Non-linear Equation Based on Steepest Descent Method

Abstract

This paper concerns with the problem of solving non-linear equation. It is shown that solving non-linear equation is equivalent to the evaluation extremum of funtion. In terms of unconstrained optimization using steepest descent method, we propose an algorithm for solving non-linear equation. It is shown that the proposed algorithm has the same convergence rate as the secant method. Several numerical experiments are also provided to demonstrate the effect of the proposed algorithm.