A modification of Muller's method

It is well-known that Muller's method for the computation of the zeros of continuous functions has order approximate to 1.84 [10], and does not have the character of global convergence. Muller's method is based on the interpolating polynomial built on the last three points of the iterative sequence. In this paper the authors take as nodes of the interpolating polynomial the last two points of the sequence and the middle point between them. The resulting method has order p = 2 for regular functions. This method leads to a globally convergent algorithm because it uses dichotomic techniques. Many numerical examples are given to show how the proposed code improves on Muller's method.