An efficient algorithm for global interval solution of nonlinear algebraic equations and its GPGPU implementation

TL;DR

This paper introduces a GPU-accelerated algorithm for globally solving nonlinear algebraic equations with real interval solutions, significantly improving efficiency and accuracy over traditional serial methods, especially for problems with more than six variables.

Contribution

The paper presents a novel GPGPU-based algorithm that globally searches for real solutions of nonlinear algebraic equations, addressing efficiency issues in high-variable scenarios.

Findings

The GPU implementation achieves faster solution times than serial methods.

The method maintains high accuracy in solutions.

It effectively handles equations with more than six variables.

Abstract

Solving nonlinear algebraic equations is a classic mathematics problem, and common in scientific researches and engineering applications. There are many numeric, symbolic and numeric-symbolic methods of solving (real) solutions. Unlucky, these methods are constrained by some factors, e.g., high complexity, slow serial calculation, and the notorious intermediate expression expansion. Especially when the count of variables is larger than six, the efficiency is decreasing drastically. In this paper, according to the property of physical world, we pay attention to nonlinear algebraic equations whose variables are in fixed constraints, and get meaningful real solutions. Combining with parallelism of GPGPU, we present an efficient algorithm, by searching the solution space globally and solving the nonlinear algebraic equations with real interval solutions. Furthermore, we realize the Hansen-Sengupta method on GPGPU. The experiments show that our method can solve many nonlinear algebraic equations, and the results are accurate and more efficient compared to traditional serial methods.