Approximate multivariate polynomial factorization based on zero-sum relations

Authors:
Tateaki Sasaki
Affiliations:
Univ. of Tsukuba, Ibaraki, Japan
Venue:
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Year:
2001

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Abstract

Conventional algorithms for approximate factorization of multivariate polynomial suffer from a dilemma: a polynomial-time algorithm which is based on zero-sum relations among power-series roots is practically very time-consuming and unstable, while practically stable algorithms are of combinatorial nature. In this paper, we present two ideas: one is a numeric matrix manipulation method to find zero-sum relations efficiently and the other is a method to utilize power-series roots expanded at different points. We analyze the methods theoretically and investigate their practicality by applying to several examples. We also discuss numerical stability of the matrix method.