Multivariate polynomial perturbations of algebraic equations

K Avrachenkov, V Ejov, Jerzy Filar

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)


    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.

    Original languageEnglish
    Pages (from-to)214-221
    Number of pages8
    JournalJournal of Mathematical Analysis and Applications
    Issue number1
    Publication statusPublished - Sept 2010


    • Algebraic equations
    • Multivariate perturbation
    • Newton polygon
    • Weighted PageRank


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