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

Numerical methods based on interval arithmetic are efficient means to reliably solve nonlinear systems of equa-tions. 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 eas-ily 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