Polynomial algebra for Birkhoff interpolants

被引：12

作者：

Butcher, John C. ^{[2
]}

Corless, Robert M. ^{[1
]}

Gonzalez-Vega, Laureano ^{[3
]}

Shakoori, Azar ^{[3
]}

机构：

[1] Univ Western Ontario, Dept Appl Math, London, ON N6A 5B7, Canada

[2] Univ Auckland, Dept Math, Auckland, New Zealand

[3] Univ Cantabria, Dept Matemat Estadist & Comp, Santander 39071, Spain

来源：

NUMERICAL ALGORITHMS | 2011年 / 56卷 / 03期

关键词：

Lagrange; Hermite; and Hermite-Birkhoff interpolation; Contour integrals; Barycentric form; Fixed-denominator rational interpolation; Root-finding; FINITE-DIFFERENCE METHOD; ALGORITHMS; EXPANSION; INVERSION;

D O I：

10.1007/s11075-010-9385-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a unifying formulation of a number of related problems which can all be solved using a contour integral formula. Each of these problems requires finding a non-trivial linear combination of possibly some of the values of a function f, and possibly some of its derivatives, at a number of data points. This linear combination is required to have zero value when f is a polynomial of up to a specific degree p. Examples of this type of problem include Lagrange, Hermite and Hermite-Birkhoff interpolation; fixed-denominator rational interpolation; and various numerical quadrature and differentiation formulae. Other applications include the estimation of missing data and root-finding.

引用

页码：319 / 347

页数：29

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