### 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.

Original language | English |
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Pages (from-to) | 214-221 |

Number of pages | 8 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 369 |

Issue number | 1 |

DOIs | |

Publication status | Published - Sep 2010 |

### Keywords

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

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## Cite this

*Journal of Mathematical Analysis and Applications*,

*369*(1), 214-221. https://doi.org/10.1016/j.jmaa.2010.02.026