A new hybrid iteration method for solving algebraic equations

Abstract

A new hybrid iteration method (the hybrid’s name was used by Luo [Xing-Guo Luo, Applied Mathematics and Computation 171 (2) (2005) 1171–1183]) has been proposed for solving a non linear algebraic equation f( x) = 0, by using Taylor’s theorem. In this paper, we proposed a new hybrid iteration method and we show by one equation that this new hybrid iteration method is more quickly convergent than Newton’s method and hence than hybrid iteration method.