NDLI: Shape preservation of scientific data through rational fractal splines

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Shape preservation of scientific data through rational fractal splines

Content Provider	Springer Nature Link
Author	Navascués, M. A. Chand, A. K. B. Vijender, N.
Copyright Year	2013
Abstract	Fractal interpolation is a modern technique in approximation theory to fit and analyze scientific data. We develop a new class of $$\mathcal C ^1$$ - rational cubic fractal interpolation functions, where the associated iterated function system uses rational functions of the form $$\frac{p_i(x)}{q_i(x)},$$ where $$p_i(x)$$ and $$q_i(x)$$ are cubic polynomials involving two shape parameters. The rational cubic iterated function system scheme provides an additional freedom over the classical rational cubic interpolants due to the presence of the scaling factors and shape parameters. The classical rational cubic functions are obtained as a special case of the developed fractal interpolants. An upper bound of the uniform error of the rational cubic fractal interpolation function with an original function in $$\mathcal C ^2$$ is deduced for the convergence results. The rational fractal scheme is computationally economical, very much local, moderately local or global depending on the scaling factors and shape parameters. Appropriate restrictions on the scaling factors and shape parameters give sufficient conditions for a shape preserving rational cubic fractal interpolation function so that it is monotonic, positive, and convex if the data set is monotonic, positive, and convex, respectively. A visual illustration of the shape preserving fractal curves is provided to support our theoretical results.
Ending Page	362
Page Count	34
Starting Page	329
File Format	PDF
ISSN	00080624
e-ISSN	11265434
Journal	CALCOLO
Issue Number	2
Volume Number	51
Language	English
Publisher	Springer Milan
Publisher Date	2013-05-22
Publisher Place	Milan
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Monotonic functions, generalizations Smoothing, curve fitting Splines Iterated function systems Positivity Rational cubic interpolation Fractals Theory of Computation Rational cubic fractal functions Fractal interpolation functions Approximation by rational functions Interpolation Convexity, generalizations Numerical Analysis Convexity Monotonicity Rate of convergence, degree of approximation
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory Computational Mathematics

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