Approximate multivariate polynomial factorization based on zero-sum relations
Tateaki Sasaki · 2001
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.