On the roots of certain polynomials arising from the analysis of the Nelder-Mead simplex method

被引：5

作者：

Han, LX ^{[1
]}

Neumann, M

Xu, JH

机构：

[1] Univ Michigan, Dept Math, Flint, MI 48502 USA

[2] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2003年 / 363卷

关键词：

polynomials; roots; Schur-Cohn criterion; Nelder-Mead simplex method;

D O I：

10.1016/S0024-3795(02)00485-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The study of the effect of dimensionality on the Nelder-Mead simplex method for unconstrained optimization leads us to the study of a two parameter family of polynomials of the form p(n) (z) = b - az - (. . .) - az(n-1) + Z(n). We show that provided that (a) over bar - a (b) over bar is real, it is possible to use, primarily, the Schur-Cohn Criterion in order to determine the configuration of the roots of P-n (z) with respect to the unit circle. (C) 2002 Elsevier Science Inc. All rights reserved.

引用

页码：109 / 124

页数：16

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