High-Order Approximation of Set-Valued Functions

Nira Dyn; Elza Farkhi; Alona Mokhov

doi:10.1007/s00365-022-09572-7

High-Order Approximation of Set-Valued Functions

Nira Dyn, Elza Farkhi, Alona Mokhov

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce the notion of metric divided differences of set-valued functions. With this notion we obtain bounds on the error in set-valued metric polynomial interpolation. These error bounds lead to high-order approximations of set-valued functions by metric piecewise-polynomial interpolants of high degree. Moreover, we derive high-order approximation of set-valued functions by local metric approximation operators reproducing high-degree polynomials.

Original language	English
Pages (from-to)	521-546
Number of pages	26
Journal	Constructive Approximation
Volume	57
Issue number	2
DOIs	https://doi.org/10.1007/s00365-022-09572-7
State	Published - Apr 2023

Keywords

High-order approximation
Metric linear combinations
Metric local linear operators
Set-valued functions
Set-valued metric divided differences
Set-valued metric polynomial interpolation

All Science Journal Classification (ASJC) codes

Computational Mathematics
Analysis
General Mathematics

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10.1007/s00365-022-09572-7

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title = "High-Order Approximation of Set-Valued Functions",

abstract = "We introduce the notion of metric divided differences of set-valued functions. With this notion we obtain bounds on the error in set-valued metric polynomial interpolation. These error bounds lead to high-order approximations of set-valued functions by metric piecewise-polynomial interpolants of high degree. Moreover, we derive high-order approximation of set-valued functions by local metric approximation operators reproducing high-degree polynomials.",

keywords = "High-order approximation, Metric linear combinations, Metric local linear operators, Set-valued functions, Set-valued metric divided differences, Set-valued metric polynomial interpolation",

author = "Nira Dyn and Elza Farkhi and Alona Mokhov",

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AU - Farkhi, Elza

AU - Mokhov, Alona

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N2 - We introduce the notion of metric divided differences of set-valued functions. With this notion we obtain bounds on the error in set-valued metric polynomial interpolation. These error bounds lead to high-order approximations of set-valued functions by metric piecewise-polynomial interpolants of high degree. Moreover, we derive high-order approximation of set-valued functions by local metric approximation operators reproducing high-degree polynomials.

AB - We introduce the notion of metric divided differences of set-valued functions. With this notion we obtain bounds on the error in set-valued metric polynomial interpolation. These error bounds lead to high-order approximations of set-valued functions by metric piecewise-polynomial interpolants of high degree. Moreover, we derive high-order approximation of set-valued functions by local metric approximation operators reproducing high-degree polynomials.

KW - High-order approximation

KW - Metric linear combinations

KW - Metric local linear operators

KW - Set-valued functions

KW - Set-valued metric divided differences

KW - Set-valued metric polynomial interpolation

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DO - 10.1007/s00365-022-09572-7

M3 - مقالة

SN - 0176-4276

VL - 57

SP - 521

EP - 546

JO - Constructive Approximation

JF - Constructive Approximation

IS - 2

ER -

High-Order Approximation of Set-Valued Functions

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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