同时Padé逼近的算法
Algorithms for Simultaneous Padé Approximations
摘要：
我们描述了如何解决同时Padé近似的幂级数环$K[[x]]$的字段$K$使用$O~(n^{ω- 1} d)$操作在$K$，其中$d$是寻求的精度和$n$是幂级数近似的数量。我们开发了两种算法，使用不同的方法。这两种算法都返回一个减少的子基，生成满足给定度约束的输入近似问题的完整解集。我们的结果是可能的最小逼近基和Hermite Padé近似的快速计算最近的突破。
英文摘要：
We describe how to solve simultaneous Padé approximations over a power series ring $K[[x]]$ for a field $K$ using $O~(n^{ω- 1} d)$ operations in $K$, where $d$ is the sought precision and $n$ is the number of power series to approximate. We develop two algorithms using different approaches. Both algorithms return a reduced sub-bases that generates the complete set of solutions to the input approximations problem that satisfy the given degree constraints. Our results are made possible by recent breakthroughs in fast computations of minimal approximant bases and Hermite Padé approximations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
