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Mathematics of Computation

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Shepard-Bernoulli operators


Authors: R. Caira and F. Dell'Accio
Journal: Math. Comp. 76 (2007), 299-321
MSC (2000): Primary 41A05, 41A25; Secondary 65D05
Published electronically: August 8, 2006
MathSciNet review: 2261023
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Abstract: We introduce the Shepard-Bernoulli operator as a combination of the Shepard operator with a new univariate interpolation operator: the generalized Taylor polynomial. Some properties and the rate of convergence of the new combined operator are studied and compared with those given for classical combined Shepard operators. An application to the interpolation of discrete solutions of initial value problems is given.


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Additional Information

R. Caira
Affiliation: Dipartimento di Matematica, Università della Calabria, 87036 Rende (Cs), Italy
Email: caira@unical.it

F. Dell'Accio
Affiliation: Dipartimento di Matematica, Università della Calabria, 87036 Rende (Cs), Italy
Email: fdellacc@unical.it

DOI: https://doi.org/10.1090/S0025-5718-06-01894-1
Keywords: Univariate interpolation, combined Shepard operator, degree of exactness, rate of convergence
Received by editor(s): November 4, 2004
Received by editor(s) in revised form: June 3, 2005
Published electronically: August 8, 2006
Article copyright: © Copyright 2006 American Mathematical Society