Evaluation of interval extension of the power function by graph decomposition

TL;DR

This paper presents a method for accurately evaluating the interval extension of the power function x^y by decomposing its graph, simplifying the computation for all real x and y.

Contribution

It introduces a graph decomposition approach that reduces the complexity of interval extension evaluation for the power function without constraints on x and y.

Findings

The method simplifies interval extension evaluation for all real x and y.

Graph decomposition enables accurate computation without restrictions.

The approach reduces computational complexity compared to previous methods.

Abstract

The subject of our talk is the correct evaluation of interval extension of the function specified by the expression x^y without any constraints on the values of x and y. The core of our approach is a decomposition of the graph of x^y into a small number of parts which can be transformed into subsets of the graph of x^y for non-negative bases x. Because of this fact, evaluation of interval extension of x^y, without any constraints on x and y, is not much harder than evaluation of interval extension of x^y for non-negative bases x.