Note on improvement precision of recursive function simulation in floating point standard

TL;DR

This paper proposes a new rounding method that improves the precision of recursive function simulations in IEEE floating point standard, reducing errors and preventing divergence in chaotic maps.

Contribution

It introduces a novel averaging rounding technique that enhances precision and stability in recursive function simulations within the IEEE floating point standard.

Findings

Improves one digit of precision in recursive function simulations.

Reduces divergence in logistic map simulations.

Numerical results demonstrate enhanced accuracy and stability.

Abstract

An improvement on precision of recursive function simulation in IEEE floating point standard is presented. It is shown that the average of rounding towards negative infinite and rounding towards positive infinite yields a better result than the usual standard rounding to the nearest in the simulation of recursive functions. In general, the method improves one digit of precision and it has also been useful to avoid divergence from a correct stationary regime in the logistic map. Numerical studies are presented to illustrate the method.