Abstract
Based on the Taylor's expansion of an inverse function, we extend the Schröder'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.
Acknowledgements
This work has been financially supported by an individual discovery grant from NSERC (Natural Sciences and Engineering Research Council of Canada).