Fixed Point Acceleration in R

Authors

Stuart Baumann
Margaryta Klymak, University of Oxford

Date of this Version

6-2019

Document Type

Article

Citation

The R Journal (June 2019) 11(1); Editor: Norm Matloff

Comments

Copyright 2019, The R Foundation. Open access material. License: CC BY 4.0 International

Abstract

t A fixed point problem is one where we seek a vector, X, for a function, f, such that f(X) = X. The solution of many such problems can be accelerated by using a fixed point acceleration algorithm. With the release of the FixedPoint package there is now a number of algorithms available in R that can be used for accelerating the finding of a fixed point of a function. These algorithms include Newton acceleration, Aitken acceleration and Anderson acceleration as well as epsilon extrapolation methods and minimal polynomial methods. This paper demonstrates the use of fixed point accelerators in solving numerical mathematics problems using the algorithms of the FixedPoint package as well as the squarem method of the SQUAREM package.