A modified trust region algorithm for nonlinear equations with new updating rule of trust region radius

Jinyan Fan; Jianyu Pan

doi:10.1080/00207160802691645

A modified trust region algorithm for nonlinear equations with new updating rule of trust region radius

Jinyan Fan^*
, Jianyu Pan

^*此作品的通讯作者

数学科学学院

Shanghai Jiao Tong University

科研成果: 期刊稿件 › 文章 › 同行评审

17 引用（Scopus）

摘要

In this article, we present a trust region algorithm for the nonlinear equations with a new updating rule of the trust region radius, which takes some function of the residual. We show that under the local error bound condition which is weaker than the non-singularity, the new algorithm converges quadratically to some solution of the nonlinear equations. Numerical results show that the new algorithm performs very well for some singular nonlinear equations.

源语言	英语
页（从-至）	3186-3195
页数	10
期刊	International Journal of Computer Mathematics
卷	87
期	14
DOI	https://doi.org/10.1080/00207160802691645
出版状态	已出版 - 11月 2010

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10.1080/00207160802691645

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abstract = "In this article, we present a trust region algorithm for the nonlinear equations with a new updating rule of the trust region radius, which takes some function of the residual. We show that under the local error bound condition which is weaker than the non-singularity, the new algorithm converges quadratically to some solution of the nonlinear equations. Numerical results show that the new algorithm performs very well for some singular nonlinear equations.",

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AB - In this article, we present a trust region algorithm for the nonlinear equations with a new updating rule of the trust region radius, which takes some function of the residual. We show that under the local error bound condition which is weaker than the non-singularity, the new algorithm converges quadratically to some solution of the nonlinear equations. Numerical results show that the new algorithm performs very well for some singular nonlinear equations.

KW - local error bound condition

KW - nonlinear equations

KW - quadratic convergence

KW - trust region method

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M3 - 文章

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A modified trust region algorithm for nonlinear equations with new updating rule of trust region radius

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