LAUSR

In this paper, we present, analyze, and test a family of high order iterative methods for finding simple and multiple roots of nonlinear algebraic equations of the form $$f(x)=0$$f(x)=0. The proposed method can achieve convergence of order p, where $$p\ge 2$$p≥2 is a positive integer. The standard Newton–Raphson method ($$p=2$$p=2) and the Chebyshev’s method ($$p=3$$p=3) are both special cases of this family of methods. The pth order method requires evaluation of the function and its derivative up to order $$p-1$$p-1 at each step. Several numerical experiments are provided to validate the theoretical order of convergence for nonlinear functions with simple and multiple roots.