Numerical method for real root isolation of semi-algebraic system and its applications

TL;DR

This paper introduces an efficient numerical algorithm combining homotopy continuation and interval Newton methods to isolate real roots of semi-algebraic systems, significantly reducing computational costs compared to traditional symbolic methods.

Contribution

The paper presents a novel numerical approach that effectively isolates real roots of semi-algebraic systems, outperforming existing symbolic techniques in efficiency.

Findings

Reduces computational cost substantially

Effective on systems with transcendental functions

Validated on random and application-specific examples

Abstract

In this paper, based on the homotopy continuation method and the interval Newton method, an efficient algorithm is introduced to isolate the real roots of semi-algebraic system. Tests on some random examples and a variety of problems including transcendental functions arising in many applications show that the new algorithm reduces the cost substantially compared with the traditional symbolic approaches.