Two-point Pade approximation to Herglotz-Riesz transforms

被引：2

作者：

Bultheel, Adhemar ^{[1
]}

Mendoza, Carlos Diaz ^{[2
]}

机构：

[1] Katholieke Univ Leuven, Dept Comp Sci, Celestijnenlaan 200A, B-3001 Leuven, Heverlee, Belgium

[2] Laguna Univ, Dept Math Anal, Tenerife 38271, Spain

来源：

NUMERICAL ALGORITHMS | 2023年 / 92卷 / 01期

关键词：

Pade approximation; Herglotz-Riesz transform; Caratheodory function; Stieltjes polynomial; Quasi-paraorthogonal; Unit circle; CONVERGENCE; QUADRATURE; POLYNOMIALS; TABLE;

D O I：

10.1007/s11075-022-01467-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Pade approximation is the rational generalization of Hermite interpolating polynomial. On its own merits, it has earned a relevant place in the theory of constructive approximation. In this article, we will develop an exhaustive analysis of two-point Pade approximations to Herglotz-Riesz transforms. We study the convergence problem when the poles are partially preassigned. In this analysis, the Stieltjes polynomials on the unit circle naturally arise. Finally, some illustrative numerical examples are discussed.

引用

页码：269 / 299

页数：31

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