A Data-Parallel Algorithm to Reliably Solve Systems of Nonlinear Equations

TL;DR

This paper introduces a new, simpler, and faster data-parallel algorithm for solving nonlinear systems of equations using interval arithmetic, significantly improving performance over existing methods.

Contribution

The paper presents a novel, more efficient, and easily parallelizable algorithm for enforcing box consistency in solving nonlinear equations, outperforming previous methods like bc3revise.

Findings

Achieves up to an order of magnitude speedup with SIMD parallelization.

Simpler algorithm compared to bc3revise.

Effective in solving difficult nonlinear systems.

Abstract

Numerical methods based on interval arithmetic are efficient means to reliably solve nonlinear systems of equations. Algorithm bc3revise is an interval method that tightens variables' domains by enforcing a property called box consistency. It has been successfully used on difficult problems whose solving eluded traditional numerical methods. We present a new algorithm to enforce box consistency that is simpler than bc3revise, faster, and easily data parallelizable. A parallel implementation with Intel SSE2 SIMD instructions shows that an increase in performance of up to an order of magnitude and more is achievable.