TY - JOUR
T1 - High-Order Approximation of Set-Valued Functions
AU - Dyn, Nira
AU - Farkhi, Elza
AU - Mokhov, Alona
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2023/4
Y1 - 2023/4
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
UR - http://www.scopus.com/inward/record.url?scp=85130723808&partnerID=8YFLogxK
U2 - 10.1007/s00365-022-09572-7
DO - 10.1007/s00365-022-09572-7
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AN - SCOPUS:85130723808
SN - 0176-4276
VL - 57
SP - 521
EP - 546
JO - Constructive Approximation
JF - Constructive Approximation
IS - 2
ER -