TITLE

# Rational Cubic Spline for Positivity Preserving Interpolation

AUTHOR(S)
Samsul Ariffin Abdul Karim
PUB. DATE
June 2014
SOURCE
Australian Journal of Basic & Applied Sciences;Jun2014, Vol. 8 Issue 9, p493
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
Background: A rational cubic spline scheme is developed with cubic spline as numerator and cubic Ball function as denominator. The two parameters, in the description of the rational interpolant, have been constrained to preserve the shape of the data. The positivity-preserving properties of this rational interpolant, to a given data set are shown. The degree of smoothness C1 is attained (first order of parametric continuity). Objective: Preserving the positive data by using new rational cubic spline and produces the positivee interpolating curves. Results: The sufficient condition for the rational cubic interpolant to be positive are derived and from the numerical results the propose rational cubic spline interpolant gives comparable results. Conclusion: The sufficient condition for positivity constraints were restricted on two shape parameters vi and wi to assure the positivity of the data will be preserved completely. The solution to the shape preserving spline is always exists. We conclude that, the developed scheme work well and is comparable to the existing schemes. It also provides good alternative to the existing rational spline for shape preserving interpolation problem.
ACCESSION #
97368453

## Related Articles

• A New Error Bound for Shifted Surface Spline Interpolation. Lin-Tian Luh // Studies in Mathematical Sciences;Nov2010, Vol. 1 Issue 1, p1

Shifted surface spline is a frequently used radial function for scattered data interpolation. The most frequently used error bounds for this radial function are the one raised by Wu and Schaback in  and the one raised by Madych and Nelson in . Both are O(dl) as d â†’ 0, where l is a...

• Multivariate interpolation with increasingly flat radial basis functions of finite smoothness. Song, Guohui; Riddle, John; Fasshauer, Gregory; Hickernell, Fred // Advances in Computational Mathematics;Apr2012, Vol. 36 Issue 3, p485

In this paper, we consider multivariate interpolation with radial basis functions of finite smoothness. In particular, we show that interpolants by radial basis functions in â„ with finite smoothness of even order converge to a polyharmonic spline interpolant as the scale parameter of the...

• The influence of the smoothness of interpolating trigonometric splines on interpolation error. Denysiuk, Volodymyr; Negodenko, Elena // Ukrainian Food Journal;2013, Vol. 2 Issue 4, p570

Introduction. The theory of algebraic interpolated polynomials has some drawbacks: the older members of polynomials rapidly increase with the degree of polynomials used; they rarely leads to any reasonable physical interpretation of the obtained approximations. When modeling it is acute to apply...

• Convexity Preserving Interpolation by GCÂ²-Rational Cubic Spline. Dube, M.; Rana, P. S. // International Journal of Computer Applications;Dec2013, Vol. 84, p1

A weighted rational cubic spline interpolation has been constructed using rational spline with quadratic denominator. GC1-piecewise rational cubic spline function involving parameters has been constructed which produces a monotonic interpolant to given monotonic data . The degree of smoothness...

• Approximation by rational spline functions. Tachev, Gancho // Calcolo;Dec2006, Vol. 43 Issue 4, p279

We discuss the linear precision property of NURBS functions. The degree of approximation of continuous functions is studied. Keywords: NURBS functions; linear precision; approximation degree; modulus of smoothness Mathematics Subject Classification (1991): 41A15, 41A25, 41A28, 41A36, 41A63,...

• Calibration relations for B-splines of fourth order. Dem'yanovich, Yu.; Miroshnichenko, I. // Journal of Mathematical Sciences;Nov2011, Vol. 178 Issue 6, p576

We study necessary and sufficient conditions for the smoothness of (not necessarily polynomial) splines of fourth order. We establish the uniqueness of a space of splines of maximal smoothness and prove embeddings on refined grids. We also obtain the corresponding calibration relations....

• Local Lagrange Interpolation with Bivariate Splines of Arbitrary Smoothness. Nürbberger, Günther; Rayevskaya, Vera; Schumaker, Larry L.; Zeilfelder, Frank // Constructive Approximation;Nov2005, Vol. 23 Issue 1, p33

We describe a method which can be used lo interpolate function values at a set ot scattered points in a planar domain using bivariate polynomial splines of any prescribed smoothness. The method starts with an arbitrary given triangulation of the data points, and involves refining sonic of the...

• Local Hermite Interpolation by Bivariate CÂ¹ Cubic Splines on Checkerboard Triangulations. Sun-Kang Chen; Huan-Wen Liu; Xiang-Zhao Cui // Journal of Computational Analysis & Applications;Jan2012, Vol. 14 Issue 1, p559

Given a so-call checkerboard quadrangulation â—ŠÌ„, a checkerboard triangulation â€¦ can be obtained by adding two diagonals of all quadrilaterals in â—ŠÌ„. In this paper, we develop a local Hermite interpolation method for bivariate CÂ¹ cubic splines on â€¦. By enforcing...

• SMOOTH SUPPORT VECTOR REGRESSION BASED ON MODIFICATION SPLINE INTERPOLATION. BIN REN; HUIJIE LIU; LEI YANG; LIANGLUN CHENG // Journal of Theoretical & Applied Information Technology;10/15/2012, Vol. 44 Issue 1, p92

Regression analysis is often formulated as an optimization problem with squared loss functions. Facing the challenge of the selection of the proper function class with polynomial smooth techniques applied to Support Vector Regression models, this study takes three interplation points spline...

Share