Lacunary Interpolation by Fractal Splines with Variable Scaling Parameters. Issue 1 (20th February 2017)

• Record Type: Journal Article
• Authors: Viswanathan, P.; Chand, A.K.B.; Tyada, K.R.
• Is Part Of: Numerical mathematics. Volume 10:Issue 1(2017)
• Page Start: 65
• Page End: 83
• Publication Date: 2017-02-20
• Subjects: 28A80, -- 41A05, -- 41A15, -- 41A25; lacunary interpolation, -- fractal interpolation function, -- variable scaling parameters, -- Meir-Sharma quintic spline, -- convergence; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.4208/nmtma.2017.m1514
• Languages: English
• ISSNs: 1004-8979

Abstract

Abstract: For a prescribed set of lacunary data with equally spaced knot sequence in the unit interval, we show the existence of a family of fractal splines satisfying for v = 0, 1, …, N and suitable boundary conditions. To this end, the unique quintic spline introduced by A. Meir and A. Sharma [SIAM J. Numer. Anal. 10(3) 1973, pp. 433-442] is generalized by using fractal functions with variable scaling parameters. The presence of scaling parameters that add extra "degrees of freedom", self-referentiality of the interpolant, and "fractality" of the third derivative of the interpolant are additional features in the fractal version, which may be advantageous in applications. If the lacunary data is generated from a function Φ satisfying certain smoothness condition, then for suitable choices of scaling factors, the corresponding fractal spline satisfies, as the number of partition points increases.