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

Author

Goualard, Frédéric ; Goldsztejn, Alexandre

Author_Institution

LINA, Univ. de Nantes, Nantes

fYear

2008

fDate

1-4 Dec. 2008

Firstpage

39

Lastpage

46

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.

Keywords

floating point arithmetic; mathematics computing; nonlinear equations; parallel algorithms; Intel SSE2 SIMD; bc3revise Algorithm; data-parallel algorithm; interval arithmetic; nonlinear equations; reliably solve systems; Computer aided instruction; Concurrent computing; Convergence of numerical methods; Distributed computing; Floating-point arithmetic; Iterative methods; Nonlinear equations; Nonlinear systems; Pervasive computing; Registers; SIMD algorithm; SSE2; nonlinear equation;

fLanguage

English

Publisher

ieee

Conference_Titel

Parallel and Distributed Computing, Applications and Technologies, 2008. PDCAT 2008. Ninth International Conference on

Conference_Location

Otago

Print_ISBN

978-0-7695-3443-5

Type

conf

DOI

10.1109/PDCAT.2008.26

Filename

4710959