PCG methods applied to a system of nonlinear equations

Xiaojun Chen; Tetsuro Yamamoto

doi:10.1016/0377-0427(91)90161-C

PCG methods applied to a system of nonlinear equations

Xiaojun Chen, Tetsuro Yamamoto

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

1 Citation (Scopus)

Abstract

In this paper, we consider a quasi-Newton iteration for solving a nonlinear equation F(x) = Ax + g(x) = 0 in Rn, where A is a symmetric positive definite matrix and g is a bounded continuous function. We discuss the PCG method with various preconditioners to solve the linear equation at each step of the iteration, estimate their condition numbers, and compare their computing time for a numerical example.

Original language	English
Pages (from-to)	61-75
Number of pages	15
Journal	Journal of Computational and Applied Mathematics
Volume	38
Issue number	1-3
DOIs	https://doi.org/10.1016/0377-0427(91)90161-C
Publication status	Published - 23 Dec 1991
Externally published	Yes

Keywords

Newton-like method
nonlinear equations
PCG method

ASJC Scopus subject areas

Applied Mathematics
Computational Mathematics
Numerical Analysis

More information

10.1016/0377-0427(91)90161-C

Cite this

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AB - In this paper, we consider a quasi-Newton iteration for solving a nonlinear equation F(x) = Ax + g(x) = 0 in Rn, where A is a symmetric positive definite matrix and g is a bounded continuous function. We discuss the PCG method with various preconditioners to solve the linear equation at each step of the iteration, estimate their condition numbers, and compare their computing time for a numerical example.

KW - Newton-like method

KW - nonlinear equations

KW - PCG method

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PCG methods applied to a system of nonlinear equations

Abstract

Keywords

ASJC Scopus subject areas

More information

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