Preserving convexity through rational cubic spline fractal interpolation function

详细信息    查看全文

• 作者：P. Viswanathan ; A.K.B. Ch ; R.P. Agarwal
• 关键词：65D05 ; 65D07 ; 65D10 ; 41A20 ; 28A80
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：June, 2014
• 年：2014
• 卷：263
• 期：Complete
• 页码：262-276
• 全文大小：629 K

文摘

We propose a new type of -rational cubic spline Fractal Interpolation Function (FIF) for convexity preserving univariate interpolation. The associated Iterated Function System (IFS) involves rational functions of the form , where are cubic polynomials determined through the Hermite interpolation conditions of the FIF and are preassigned quadratic polynomials with two shape parameters. The rational cubic spline FIF converges to the original function as rapidly as the th power of the mesh norm approaches to zero, provided is continuous for or and certain mild conditions on the scaling factors are imposed. Furthermore, suitable values for the rational IFS parameters are identified so that the property of convexity carries from the data set to the rational cubic FIFs. In contrast to the classical non-recursive convexity preserving interpolation schemes, the present fractal scheme is well suited for the approximation of a convex function whose derivative is continuous but has varying irregularity.