Fixed point acceleration in R

Abstract

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.