Multivariate polynomial perturbations of algebraic equations

dc.contributor.author	Avrachenkov, K.
dc.contributor.author	Ejov, V.
dc.contributor.author	Filar, J.A.
dc.date.issued	2010
dc.description.abstract	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.
dc.identifier.citation	Journal of Mathematical Analysis and Applications, 2010; 369(1):214-221
dc.identifier.doi	10.1016/j.jmaa.2010.02.026
dc.identifier.issn	0022-247X
dc.identifier.uri	https://hdl.handle.net/1959.8/89529
dc.language.iso	en
dc.publisher	Academic Press
dc.rights	Copyright status unknown
dc.source.uri	https://doi.org/10.1016/j.jmaa.2010.02.026
dc.subject	algebraic equations
dc.subject	multivariate perturbation
dc.subject	newton polygon
dc.subject	weighted pagerank
dc.title	Multivariate polynomial perturbations of algebraic equations
dc.type	Journal article
pubs.publication-status	Published
ror.mmsid	9915910582701831

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