Parallel computation of real solving bivariate polynomial systems by zero-matching method

TL;DR

This paper introduces a parallel algorithm for solving real roots of bivariate polynomial systems using a zero-matching approach, which also determines root multiplicities and can be extended to multivariate systems.

Contribution

The paper presents a novel zero-matching method for solving bivariate polynomial systems, including root multiplicities, with natural parallelization and potential for multivariate generalization.

Findings

Effective computation of real roots with multiplicities

Parallelization enhances computational efficiency

Method generalizes to multivariate systems

Abstract

We present a new algorithm for solving the real roots of a bivariate polynomial system $\Sigma=\{f(x,y),g(x,y)\}$ with a finite number of solutions by using a zero-matching method. The method is based on a lower bound for bivariate polynomial system when the system is non-zero. Moreover, the multiplicities of the roots of $\Sigma=0$ can be obtained by a given neighborhood. From this approach, the parallelization of the method arises naturally. By using a multidimensional matching method this principle can be generalized to the multivariate equation systems.