Designing General p-Ary n-Point Smooth Subdivision Schemes

2014 ◽  
Vol 472 ◽  
pp. 510-515 ◽  
Author(s):  
Hong Chan Zheng ◽  
Qian Song
Keyword(s):  
Smooth Curve ◽  
Approximation Order ◽  
Subdivision Scheme ◽  
Subdivision Schemes ◽  
Special Cases ◽  
Two Parameters ◽  
Interpolatory Subdivision

In this paper, in order to produce smooth curve, we design a class of n-point p-ary smooth interpolatory subdivision schemes that can reproduce polynomials of degree n-1 with approximation order n. Many classical interpolatory subdivision schemes are special cases of this kind of subdivision. We illustrate the approach with a new 5-point quaternary interpolatory subdivision scheme with two parameters, which reproduces polynomial of degree 4 with approximation order of 5 and can generate new interpolatory curves.

scholarly journals A New 4-PointC3Quaternary Approximating Subdivision Scheme

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Ghulam Mustafa ◽  
Faheem Khan
Keyword(s):  
Shape Parameter ◽  
Approximation Order ◽  
Subdivision Scheme ◽  
Subdivision Schemes ◽  
Approximating Subdivision Scheme

A new 4-pointC3quaternary approximating subdivision scheme with one shape parameter is proposed and analyzed. Its smoothness and approximation order are higher but support is smaller in comparison with the existing binary and ternary 4-point subdivision schemes.

Fractal range of a 3-point ternary interpolatory subdivision scheme with two parameters

2007 ◽  
Vol 32 (5) ◽  
pp. 1838-1845 ◽  
Author(s):  
Hongchan Zheng ◽  
Zhenglin Ye ◽  
Zuoping Chen ◽  
Hongxing Zhao
Keyword(s):  
Subdivision Scheme ◽  
Two Parameters ◽  
Interpolatory Subdivision

scholarly journals The Mask of Odd Pointsn-Ary Interpolating Subdivision Scheme

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Ghulam Mustafa ◽  
Jiansong Deng ◽  
Pakeeza Ashraf ◽  
Najma Abdul Rehman
Keyword(s):  
Explicit Formula ◽  
Error Bounds ◽  
Subdivision Scheme ◽  
Subdivision Schemes ◽  
Total Absolute Curvature ◽  
Absolute Curvature ◽  
Special Cases ◽  
Preservation Property ◽  
Subdivision Curves ◽  
And Control

We present an explicit formula for the mask of odd pointsn-ary, for any oddn⩾3, interpolating subdivision schemes. This formula provides the mask of lower and higher arity schemes. The 3-point and 5-pointa-ary schemes introduced by Lian, 2008, and (2m+1)-pointa-ary schemes introduced by, Lian, 2009, are special cases of our explicit formula. Moreover, other well-known existing odd pointn-ary schemes including the schemes introduced by Zheng et al., 2009, can easily be generated by our formula. In addition, error bounds between subdivision curves and control polygons of schemes are computed. It has been noticed that error bounds decrease when the complexity of the scheme decreases and vice versa. Also, as we increase arity of the schemes the error bounds decrease. Furthermore, we present brief comparison of total absolute curvature of subdivision schemes having different arity with different complexity. Convexity preservation property of scheme is also presented.

Interpolatory subdivision schemes with the optimal approximation order

2019 ◽  
Vol 347 ◽  
pp. 1-14 ◽  
Author(s):  
Baoxing Zhang ◽  
Hongchan Zheng ◽  
Weijie Song ◽  
Zengyao Lin ◽  
Jie Zhou
Keyword(s):  
Approximation Order ◽  
Optimal Approximation ◽  
Subdivision Schemes ◽  
Interpolatory Subdivision

scholarly journals Construction of a family of non-stationary combined ternary subdivision schemes reproducing exponential polynomials

2021 ◽  
Vol 19 (1) ◽  
pp. 909-926
Author(s):  
Zeze Zhang ◽  
Hongchan Zheng ◽  
Lulu Pan
Keyword(s):  
Approximation Order ◽  
High Order ◽  
Subdivision Scheme ◽  
Exponential Polynomial ◽  
Subdivision Schemes ◽  
Exponential Polynomials ◽  
Variable Parameters ◽  
Numerical Examples

Abstract In this paper, we propose a family of non-stationary combined ternary ( 2 m + 3 ) \left(2m+3) -point subdivision schemes, which possesses the property of generating/reproducing high-order exponential polynomials. This scheme is obtained by adding variable parameters on the generalized ternary subdivision scheme of order 4. For such a scheme, we investigate its support and exponential polynomial generation/reproduction and get that it can generate/reproduce certain exponential polynomials with suitable choices of the parameters and reach 2 m + 3 2m+3 approximation order. Moreover, we discuss its smoothness and show that it can produce C 2 m + 2 {C}^{2m+2} limit curves. Several numerical examples are given to show the performance of the schemes.

scholarly journals Fractional Integral Inequalities for Exponentially Nonconvex Functions and Their Applications

2021 ◽  
Vol 5 (3) ◽  
pp. 80
Author(s):  
Hari Mohan Srivastava ◽  
Artion Kashuri ◽  
Pshtiwan Othman Mohammed ◽  
Dumitru Baleanu ◽  
Y. S. Hamed
Keyword(s):  
Integral Inequalities ◽  
Fractional Integrals ◽  
Auxiliary Result ◽  
Wright Function ◽  
Nonconvex Functions ◽  
Special Cases ◽  
Type Integral ◽  
Generic Class ◽  
Two Parameters ◽  
Class Of Functions

In this paper, the authors define a new generic class of functions involving a certain modified Fox–Wright function. A useful identity using fractional integrals and this modified Fox–Wright function with two parameters is also found. Applying this as an auxiliary result, we establish some Hermite–Hadamard-type integral inequalities by using the above-mentioned class of functions. Some special cases are derived with relevant details. Moreover, in order to show the efficiency of our main results, an application for error estimation is obtained as well.

scholarly journals Convexity preservation of the four-point interpolatory subdivision scheme

1999 ◽  
Vol 16 (8) ◽  
pp. 789-792 ◽  
Author(s):  
Nira Dyn ◽  
Frans Kuijt ◽  
David Levin ◽  
Ruud van Damme
Keyword(s):  
Subdivision Scheme ◽  
Interpolatory Subdivision
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