Interpolation and cubature at geronimus nodes generated by different geronimus polynomials

Lawrence A. Harris

doi:10.1090/conm/699/14086

Interpolation and cubature at geronimus nodes generated by different geronimus polynomials

Lawrence A. Harris

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

1 Scopus citations

Abstract

We extend the definition of Geronimus nodes to include pairs of real numbers where each coordinate consists of the alternation points of a possibly different Geronimus polynomial of the same degree. We give an explicit formula for the Lagrange polynomials for these nodes that involves the reproducing kernel for the product polynomials and deduce a cubature formula for polynomials in two variables with respect to a product measure.

Original language	English
Title of host publication	Contemporary Mathematics
Pages	137-143
Number of pages	7
DOIs	https://doi.org/10.1090/conm/699/14086
State	Published - 2017

Publication series

Name	Contemporary Mathematics
Volume	699
ISSN (Print)	0271-4132
ISSN (Electronic)	1098-3627

Bibliographical note

Publisher Copyright:
© 2017 L. Harris.

ASJC Scopus subject areas

General Mathematics

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10.1090/conm/699/14086

Cite this

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abstract = "We extend the definition of Geronimus nodes to include pairs of real numbers where each coordinate consists of the alternation points of a possibly different Geronimus polynomial of the same degree. We give an explicit formula for the Lagrange polynomials for these nodes that involves the reproducing kernel for the product polynomials and deduce a cubature formula for polynomials in two variables with respect to a product measure.",

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Interpolation and cubature at geronimus nodes generated by different geronimus polynomials

Abstract

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Bibliographical note

ASJC Scopus subject areas

Access to Document

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