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Positivity preserving rational cubic trigonometric fractal interpolation functions
Published in Springer New York LLC
2015
Volume: 139
   
Pages: 187 - 202
Abstract
In this paper, we propose a family of (Formula presented.)-rational cubic trigonometric fractal interpolation function (RCTFIF) to preserve positivity inherent in a set of data. The proposed RCTFIF is a generalized fractal version of the classical rational cubic trigonometric polynomial spline of the form (Formula presented.), where pi(θ) and qi(θ) are cubic trigonometric polynomials. The RCTFIF involves a scaling factor and four shape parameters in each subinterval. The convergence of the RCTFIF towards the original function is studied. We deduce the simple data dependent sufficient conditions on the scaling factors and shape parameters associated with the (Formula presented.)-RCTFIF so that the proposed RCTFIF preserves the positivity property of the given positive data set. The first derivative of the proposed RCTFIF is irregular in a finite or dense subset of the interpolation interval, and matches with the first derivative of the classical rational trigonometric cubic interpolation function whenever all scaling factors are zero. The effects of the scaling factors and shape parameters on the RCTFIF and its first derivative are illustrated graphically. © Springer India 2015.
About the journal
JournalData powered by TypesetSpringer Proceedings in Mathematics and Statistics
PublisherData powered by TypesetSpringer New York LLC
ISSN21941009
Open AccessNo
Concepts (14)
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    Computational mechanics
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    Fractals
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    Intelligent control
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    Interpolation
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    Polynomial approximation
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    CUBIC INTERPOLATION
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    FRACTAL INTERPOLATION
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    FRACTAL INTERPOLATION FUNCTIONS
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    ITERATED FUNCTION SYSTEM
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    Positivity
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    POSITIVITY PRESERVING
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    TRIGONOMETRIC INTERPOLATION
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    TRIGONOMETRIC POLYNOMIAL
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    Rational functions