A family of new Newton-like methods

摘要

In this paper, we present a family of new Newton-like methods, which removes the severe condition f′(x)≠0 in a neighborhood of the required root imposed on Newton’s method. The new methods are quadratically convergent and moreover, have the same error equation as Newton’s method. The detailed analysis of convergence is supplied. The numerical results show that the new methods have definite practical utility.