Padé approximants and efficient analytic continuation of a power series
Padé approximants and efficient analytic continuation of a power series
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DOI：
10.1070/rm2002v057n01abeh000475
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发表时间：
2002-02
影响因子：
0.9
通讯作者：
S. Suetin
中科院分区：
文献类型：
--
作者：
S. Suetin
这一综述反映了Pade逼近理论的现状，即幂函数级数的最佳有理逼近。主要集中在这一理论的所谓反问题上，即必须根据给定的级数的某些Pade逼近序列的极点的已知渐近行为来推导出该级数的解析连续性。行序列和对角线序列就是从这个角度来研究的。给出了Gonchar和Rakhmanov关于逆性的基本结果和作者的结果。
This survey reflects the current state of the theory of Pade approximants, that is, best rational approximations of power series. The main focus is on the so-called inverse problems of this theory, in which one must make deductions about analytic continuation of a given power series on the basis of the known asymptotic behaviour of the poles of some sequence of Pade approximants of this series. Row and diagonal sequences are studied from this point of view. Gonchar's and Rakhmanov's fundamental results of inverse nature are presented along with results of the author.