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Approximation order and approximate sum rules in subdivision

Title
Approximation order and approximate sum rules in subdivision
Authors
Conti, CostanzaRomani, LuciaYoon, Jungho
Ewha Authors
윤정호
SCOPUS Author ID
윤정호scopus
Issue Date
2016
Journal Title
JOURNAL OF APPROXIMATION THEORY
ISSN
0021-9045JCR Link1096-0430JCR Link
Citation
vol. 207, pp. 380 - 401
Keywords
Subdivision schemesExponential polynomial generation and reproductionAsymptotical similarityApproximate sum rulesApproximation order
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
Several properties of stationary subdivision schemes are nowadays well understood. In particular, it is known that the polynomial generation and reproduction capability of a stationary subdivision scheme is strongly connected with sum rules, its convergence, smoothness and approximation order. The aim of this paper is to show that, in the non-stationary case, exponential polynomials and approximate sum rules play an analogous role of polynomials and sum rules in the stationary case. Indeed, in the non-stationary univariate case we are able to show the following important facts: (i) reproduction of N exponential polynomials implies approximate sum rules of order N; (ii) generation of N exponential polynomials implies approximate sum rules of order N, under the additional assumption of asymptotical similarity and reproduction of one exponential polynomial; (iii) reproduction of an N-dimensional space of exponential polynomials and asymptotical similarity imply approximation order N; (iv) the sequence of basic limit functions of a non-stationary scheme reproducing one exponential polynomial converges uniformly to the basic limit function of the asymptotically similar stationary scheme. (C) 2016 Elsevier Inc. All rights reserved.
DOI
10.1016/j.jat.2016.02.014
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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