Quadrature Based Optimal Iterative Methods with Applications in High-Precision Computing

We present a simple yet effective and applicable scheme,based on quadrature,for constructing optimal iterative methods.According to the,still unproved,Kung-Traub conjecture an optimal iterative method based on n+1 evaluations could achieve a maximum convergence order of 2n.Through quadrature,we develop optimal iterative methods of orders four and eight.The scheme can further be applied to develop iterative methods of even higher orders.Computational results demonstrate that the developed methods are efficient as compared with many well known methods.