Verification methods for nonlinear equations with saddle point functions

Xiaojun Chen; Kouji Hashimoto

doi:10.1016/S0377-0427(03)00570-3

Verification methods for nonlinear equations with saddle point functions

Xiaojun Chen
, Kouji Hashimoto

Research output: Journal article publication › Journal article › Academic research › peer-review

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.

Original language	English
Pages (from-to)	13-24
Number of pages	12
Journal	Journal of Computational and Applied Mathematics
Volume	159
Issue number	1
DOIs	https://doi.org/10.1016/S0377-0427(03)00570-3
Publication status	Published - 1 Oct 2003
Externally published	Yes

Keywords

Nonlinear equation
Saddle point matrix
Verification method

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

More information

10.1016/S0377-0427(03)00570-3

Cite this

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title = "Verification methods for nonlinear equations with saddle point functions",

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.",

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AB - 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.

KW - Nonlinear equation

KW - Saddle point matrix

KW - Verification method

UR - https://www.scopus.com/pages/publications/0141670398

U2 - 10.1016/S0377-0427(03)00570-3

DO - 10.1016/S0377-0427(03)00570-3

M3 - Journal article

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EP - 24

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JF - Journal of Computational and Applied Mathematics

IS - 1

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Verification methods for nonlinear equations with saddle point functions

Abstract

Keywords

ASJC Scopus subject areas

More information

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