Integral refinable operators exact on polynomials

Authors:
L. Gori;E. Pellegrino;E. Santi
Affiliations:
Dip. Me.Mo.Mat., University of Roma "La Sapienza", Via A. Scarpa 10, 00161 Roma, Italy;DIMEG, University of L'Aquila, P.zza E. Pontieri, 2, 67040 Monteluco Roio (AQ), Italy;DIMEG, University of L'Aquila, P.zza E. Pontieri, 2, 67040 Monteluco Roio (AQ), Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

We study integral refinable operators of integral type exact on polynomials of even degree constructed by using refinable B-bases of GP type. We prove a general theorem of existence and uniqueness. Then we study the L^p-norm of these operators and we give error bounds in approximating functions and their derivatives belonging to suitable classes. Numerical results and comparisons with other quasi-interpolatory operators having the same order of exactness on polynomial reproduction are presented.