Multivariate polynomial perturbations of algebraic equations
Date
2010
Authors
Avrachenkov, K.
Ejov, V.
Filar, J.A.
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Journal of Mathematical Analysis and Applications, 2010; 369(1):214-221
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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.
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