论文标题
Hermite-Padé多项式的Viskovatov算法
Viskovatov algorithm for Hermite-Padé polynomials
论文作者
论文摘要
我们提出了一种用于生产I型HERMite-Padé多项式的算法，用于任意$ M+1 $ 1 $正式的Power系列$ [F_0，\ dots，f_m] $，$ m \ geq1 $，$ z = 0 $ z = 0 $（$ f_j \ in {$ f_j \ in {\ mathbb c} \ nsuty pastion $ f_j \ in {非修复属性。该算法是用于构建Padé多项式的古典Viskovatov算法的直接扩展（以$ M = 1 $我们的算法与Viskovatov算法一致）。 此处提出的算法是基于复发的关系，并且具有与多个元素相对应的所有Hermite-Padé多项式的功能（k，k，k，k，dots，k，k）$，$（k+1，k，k，k，k，k，dots，k，dots，k） $（k+1，k+1，k+1，\ dots，k+1，k）$在算法产生对应于多项式$（k+1，k+1，k+1，k+1，k+1，\ dots，k+1，k+1，k+1）$的算法时已经知道了。 我们展示了如何通过适当地更改初始条件来通过此算法找到与不同多指标相对应的HERMITE-PADé多项式。 该算法可以在$ m+1 $独立评估中平行于$ n $ n $第三步。
We propose an algorithm for producing Hermite-Padé polynomials of type I for an arbitrary tuple of $m+1$ formal power series $[f_0,\dots,f_m]$, $m\geq1$, about $z=0$ ($f_j\in{\mathbb C}[[z]]$) under the assumption that the series have a certain (`general position') nondegeneracy property. This algorithm is a straightforward extension of the classical Viskovatov algorithm for construction of Padé polynomials (for $m=1$ our algorithm coincides with the Viskovatov algorithm). The algorithm proposed here is based on a recurrence relation and has the feature that all the Hermite-Padé polynomials corresponding to the multiindices $(k,k,k,\dots,k,k)$, $(k+1,k,k,\dots,k,k)$, $(k+1,k+1,k,\dots,k,k),\dots$, $(k+1,k+1,k+1,\dots,k+1,k)$ are already known by the time the algorithm produces the Hermite-Padé polynomials corresponding to the multiindex $(k+1,k+1,k+1,\dots,k+1,k+1)$. We show how the Hermite-Padé polynomials corresponding to different multiindices can be found via this algorithm by changing appropriately the initial conditions. The algorithm can be parallelized in $m+1$ independent evaluations at each $n$th step.
