Multivariate polynomial perturbations of algebraic equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:369

Article

Avrachenkov, K.²  Ejov, V.¹  Filar, J. A.¹ 

[1] Univ S Australia, Adelaide, SA 5001, Australia

[2] INRIA Sophia Antipolis, Sophia Antipolis, France

关键词: Algebraic equations;    Multivariate perturbation;    Newton polygon;    Weighted PageRank;   

DOI  :  10.1016/j.jmaa.2010.02.026

来源: Elsevier

【 摘 要 】

In this note we study multivariate perturbations of algebraic equations. In general, it is not possible to represent the perturbed solution as a Puiseux-type power series in a connected neighborhood. For the case of two perturbation parameters we provide a sufficient condition that guarantees such a representation. Then, we extend this result to the case of more than two perturbation parameters. We motivate our study by the perturbation analysis of a weighted random walk on the Web Graph. In an instance of the latter the stationary distribution of the weighted random walk, the so-called Weighted PageRank, may depend on two (or more) perturbation parameters in a manner that illustrates our theoretical development. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free