scholarly journals A New Class of Non-stationary Interpolatory Subdivision Schemes Based on Exponential Polynomials

2006 ◽  
pp. 563-570 ◽  
Author(s):  
Yoo-Joo Choi ◽  
Yeon-Ju Lee ◽  
Jungho Yoon ◽  
Byung-Gook Lee ◽  
Young J. Kim
Keyword(s):  
Subdivision Schemes ◽  
Exponential Polynomials ◽  
New Class ◽  
Interpolatory Subdivision

scholarly journals A Family of Binary Univariate Nonstationary Quasi-Interpolatory Subdivision Reproducing Exponential Polynomials

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Baoxing Zhang ◽  
Hongchan Zheng ◽  
Lulu Pan ◽  
Guohua Peng ◽  
Weijie Song
Keyword(s):  
Subdivision Schemes ◽  
Exponential Polynomials ◽  
B Spline ◽  
New Family ◽  
Interpolatory Subdivision

In this paper, by suitably using the so-called push-back operation, a connection between the approximating and interpolatory subdivision, a new family of nonstationary subdivision schemes is presented. Each scheme of this family is a quasi-interpolatory scheme and reproduces a certain space of exponential polynomials. This new family of schemes unifies and extends quite a number of the existing interpolatory schemes reproducing exponential polynomials and noninterpolatory schemes like the cubic exponential B-spline scheme. For these new schemes, we investigate their convergence, smoothness, and accuracy and show that they can reach higher smoothness orders than the interpolatory schemes with the same reproduction property and better accuracy than the exponential B-spline schemes. Several examples are given to illustrate the performance of these new schemes.

scholarly journals Unified Framework of Approximating and Interpolatory Subdivision Schemes for Construction of Class of Binary Subdivision Schemes

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Pakeeza Ashraf ◽  
Ghulam Mustafa ◽  
Abdul Ghaffar ◽  
Rida Zahra ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Hölder Continuity ◽  
Visual Performance ◽  
Holder Continuity ◽  
Unified Framework ◽  
Subdivision Schemes ◽  
New Class ◽  
Interpolatory Subdivision

In this paper, a generalized algorithm to develop a class of approximating binary subdivision schemes is presented. The proposed algorithm is based on three-point approximating binary and four-point interpolating binary subdivision schemes. It contains a parameter which classifies members of the new class of subdivision schemes. A set of efficient properties, for instance, polynomial generation and reproduction, support, continuity, and Hölder continuity, is discussed. Moreover, applications of the proposed subdivision schemes are given in order to demonstrate their variety, flexibility, and visual performance.

scholarly journals TERNARY INTERPOLATORY SUBDIVISION SCHEMES ORIGINATED FROM SPLINES

2011 ◽  
Vol 09 (04) ◽  
pp. 611-633 ◽  
Author(s):  
AMIR Z. AVERBUCH ◽  
VALERY A. ZHELUDEV ◽  
GARY B. FATAKHOV ◽  
EDUARD H. YAKUBOV
Keyword(s):  
Arbitrary Order ◽  
Rational Points ◽  
Fast Computation ◽  
Subdivision Schemes ◽  
Rational Symbols ◽  
Interpolatory Subdivision

A generic technique for construction of ternary interpolatory subdivision schemes, which is based on polynomial and discrete splines, is presented. These schemes have rational symbols. The symbols are explicitly presented in the paper. This is accompanied by a detailed description of the design of the refinement masks and by algorithms that verify the convergence of these schemes. In addition, the smoothness of the limit functions is investigated. The ternary subdivision schemes, whose construction is based on continuous splines, become tools for fast computation ofıory s of arbitrary order at triadic rational points.

Multidimensional Interpolatory Subdivision Schemes

1997 ◽  
Vol 34 (6) ◽  
pp. 2357-2381 ◽  
Author(s):  
Sherman D. Riemenschneider ◽  
Zuowei Shen
Keyword(s):  
Subdivision Schemes ◽  
Interpolatory Subdivision
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