A Modified Iterative Method for Finding The Real Roots of A Polynomial

Abstract

A more robust root finding technique using the fixed point theory is developed. This is based on the Successive Iteration method, with a different iteration function. The advantage of this method is that it is independent of the choice for the initial guess for the numerical computation. The iterative function used in this method has a very fast convergence in the range of \([-1,1]\). The root is achieved to a very high degree of accuracy in very less number of iterative steps compared to many other iterative methods. A comparison of the root achieved to a desired accuracy using our method and the successive approximation method are presented. The nature of the convergence and the stability of the root(s) is also discussed.