Verification methods for nonlinear equations with saddle point functions

Authors:
Xiaojun Chen;Kouji Hashimoto
Affiliations:
Department of Mathematical System Science, Hirosaki University, Hirosaki 036-8561, Japan;Graduate School of Mathematics, Kyushu University, Fukuoka 812-8581, Japan
Venue:
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 6th Japan--China joint seminar on numerical mathematics, university of Tsukuba, Japan, 5-9 August 2002
Year:
2003

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Abstract

This paper presents a fast verification algorithm for nonlinear equations with saddle point functions. This algorithm is based on a block decomposition of the Krawczyk-type interval operator, which can be applied to convex programming problems and nonlinear Navier-Stokes equations. We show the efficiency of this algorithm by comparing it with the Krawczyk method and the interval Newton-like method for the discretized stationary Navier-Stokes equations.