Inverse function, Taylor's expansion and extended Schroeder's processes

摘要

Based on the Taylor's expansion of an inverse function, we extend the Schroeder's process to find and improve high-order fixed-point iteration functions (IFs) for solving a nonlinear equation. We illustrate the extended processes by using them to find better iterative methods to compute the nth root and the logarithm of a strictly positive real number. IFs for inverse trigonometric function evaluations are also considered.