@InProceedings{10.1007/978-3-642-32922-7_4,
author="Mansouri, P.
and Asady, B.
and Gupta, N.",
editor="Sn{\'a}{\v{s}}el, V{\'a}clav
and Abraham, Ajith
and Corchado, Emilio S.",
title="The Combination of Bisection Method and Artificial Bee Colony Algorithm for Solving Hard Fix Point Problems",
booktitle="Soft Computing Models in Industrial and Environmental Applications",
year="2013",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="33--41",
abstract="In this work, with combination Bisection method and Artificial bee colony algorithm together(BIS-ABC), We introduce the novel iteration method to solve the real-valued fix point problem f(x){\thinspace}={\thinspace}x, x{\thinspace}∈{\thinspace}[a, b]{\thinspace}⊆{\thinspace}R. Let f(a).f(b){\thinspace}<{\thinspace}0 and there exist $\alpha${\thinspace}∈{\thinspace}[a, b], f($\alpha$){\thinspace}={\thinspace}$\alpha$. In this way, without computing derivative of function f, real-roots determined with this method that is faster than ABC algorithm. In numerical analysis, Newton-Raphson method is a method for finding successively better approximations to the simple real roots, if f{\textasciiacutex}(x                              i              ) -- 1 = 0, in i                              th               iteration, then Newton's method will terminate and we need to change initial value of a root and do algorithm again to obtain better approximate of $\alpha$. But in proposed method, we reach to solution with direct search in [a, b], that includes $\alpha$(convergence speed maybe less than of Newton's method). We illustrate this method by offering some numerical examples and compare results with ABC algorithm.",
isbn="978-3-642-32922-7"
}