Approximation order and approximate sum rules in subdivision
- 주제(키워드) Subdivision schemes , Exponential polynomial generation and reproduction , Asymptotical similarity , Approximate sum rules , Approximation order
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 ACADEMIC PRESS INC ELSEVIER SCIENCE
- 발행년도 2016
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000130512
- 본문언어 영어
- Published As http://dx.doi.org/10.1016/j.jat.2016.02.014
초록/요약
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.
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