关于用普列解常微分方程的复杂性
On the complexity of solving ordinary differential equations in terms of Puiseux series
摘要：
本文证明了用Pu_x级数求解普通多项式微分方程的二元复杂性是级数项数的单指数。Grigoriev [10]对与普通线性微分算子相关的Riccatti微分多项式给出了这样的界。本文对任意微分多项式也得到了同样的上界。该算法基于代数方程的Newton-Puixix过程的微分版本。
英文摘要：
We prove that the binary complexity of solving ordinary polynomial differential equations in terms of Puiseux series is single exponential in the number of terms in the series. Such a bound was given by Grigoriev [10] for Riccatti differential polynomials associated to ordinary linear differential operators. In this paper, we get the same bound for arbitrary differential polynomials. The algorithm is based on a differential version of the Newton-Puiseux procedure for algebraic equations.
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