[HTML][HTML] Preserving convexity through rational cubic spline fractal interpolation function
P Viswanathan, AKB Chand, RP Agarwal - Journal of Computational and …, 2014 - Elsevier
P Viswanathan, AKB Chand, RP Agarwal
Journal of Computational and Applied Mathematics, 2014•ElsevierWe propose a new type of C 1-rational cubic spline Fractal Interpolation Function (FIF) for
convexity preserving univariate interpolation. The associated Iterated Function System (IFS)
involves rational functions of the form P n (x) Q n (x), where P n (x) are cubic polynomials
determined through the Hermite interpolation conditions of the FIF and Q n (x) are
preassigned quadratic polynomials with two shape parameters. The rational cubic spline FIF
converges to the original function Φ as rapidly as the r th power of the mesh norm …
convexity preserving univariate interpolation. The associated Iterated Function System (IFS)
involves rational functions of the form P n (x) Q n (x), where P n (x) are cubic polynomials
determined through the Hermite interpolation conditions of the FIF and Q n (x) are
preassigned quadratic polynomials with two shape parameters. The rational cubic spline FIF
converges to the original function Φ as rapidly as the r th power of the mesh norm …
We propose a new type of C 1-rational cubic spline Fractal Interpolation Function (FIF) for convexity preserving univariate interpolation. The associated Iterated Function System (IFS) involves rational functions of the form P n (x) Q n (x), where P n (x) are cubic polynomials determined through the Hermite interpolation conditions of the FIF and Q n (x) are preassigned quadratic polynomials with two shape parameters. The rational cubic spline FIF converges to the original function Φ as rapidly as the r th power of the mesh norm approaches to zero, provided Φ (r) is continuous for r= 1 or 2 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 Φ whose derivative is continuous but has varying irregularity.
Elsevier
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