Lagrange interpolation on extended generalized Jacobi nodes

Jürgen Prestin

doi:10.1007/BF02215680

Lagrange interpolation on extended generalized Jacobi nodes

Jürgen Prestin^*

^*Corresponding author for this work

Institute of Mathematics

3 Citations (Scopus)

Abstract

We consider the L^p-convergence of interpolatory processes for nonsmooth functions. Therefore we use generalizations of the well-known Marcinkiewicz-Zygmund inequality for trigonometric polynomials to the case of algebraic polynomials, extending a result of Y. Xu. Particularly, we obtain the order of convergence for certain Lagrange and quasi-Lagrange interpolatory processes on generalized Jacobi nodes. Our approach enables us also to discuss the influence of additional nodes near the endpoints ±1.

Original language	English
Journal	Numerical Algorithms
Volume	5
Issue number	3
Pages (from-to)	179-190
Number of pages	12
ISSN	1017-1398
DOIs	https://doi.org/10.1007/BF02215680
Publication status	Published - 01.03.1993

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title = "Lagrange interpolation on extended generalized Jacobi nodes",

abstract = "We consider the Lp-convergence of interpolatory processes for nonsmooth functions. Therefore we use generalizations of the well-known Marcinkiewicz-Zygmund inequality for trigonometric polynomials to the case of algebraic polynomials, extending a result of Y. Xu. Particularly, we obtain the order of convergence for certain Lagrange and quasi-Lagrange interpolatory processes on generalized Jacobi nodes. Our approach enables us also to discuss the influence of additional nodes near the endpoints ±1.",

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N2 - We consider the Lp-convergence of interpolatory processes for nonsmooth functions. Therefore we use generalizations of the well-known Marcinkiewicz-Zygmund inequality for trigonometric polynomials to the case of algebraic polynomials, extending a result of Y. Xu. Particularly, we obtain the order of convergence for certain Lagrange and quasi-Lagrange interpolatory processes on generalized Jacobi nodes. Our approach enables us also to discuss the influence of additional nodes near the endpoints ±1.

AB - We consider the Lp-convergence of interpolatory processes for nonsmooth functions. Therefore we use generalizations of the well-known Marcinkiewicz-Zygmund inequality for trigonometric polynomials to the case of algebraic polynomials, extending a result of Y. Xu. Particularly, we obtain the order of convergence for certain Lagrange and quasi-Lagrange interpolatory processes on generalized Jacobi nodes. Our approach enables us also to discuss the influence of additional nodes near the endpoints ±1.

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U2 - 10.1007/BF02215680

DO - 10.1007/BF02215680

M3 - Journal articles

AN - SCOPUS:0039516485

SN - 1017-1398

VL - 5

SP - 179

EP - 190

JO - Numerical Algorithms

JF - Numerical Algorithms

IS - 3

ER -

Lagrange interpolation on extended generalized Jacobi nodes

Abstract

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