RATIONAL APPROXIMATION TO FORMAL POWER-SERIES

被引：38

作者：

BREZINSKI, C

机构：

[1] U.E.R. I.E.E.A. - Informatique, Université des Sciences et Techniques de Lille, 59650 Villeneuve d'Ascq

来源：

JOURNAL OF APPROXIMATION THEORY | 1979年 / 25卷 / 04期

关键词：

D O I：

10.1016/0021-9045(79)90019-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A general method for obtaining rational approximations to formal power series is defined and studied. This method is based on approximate quadrature formulas. Newton-Cotes and Gauss quadrature methods are used. It is shown that Padé approximants and the ε{lunate}-algorithm are related to Gaussian formulas while linear summation processes are related to Newton-Cotes formulas. An example is exhibited which shows that Padé approximation is not always optimal. An application to e-t is studied and a method for Laplace transform inversion is proposed. © 1979.

引用

页码：295 / 317

页数：23

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