A \(\mathcal{C}^{1}\)-rational cubic fractal interpolation function: convergence and associated parameter identification problem

DOI10.1007/s10440-014-9882-3zbMath1317.28025OpenAlexW2023248833MaRDI QIDQ2352151

Puthan Veedu Viswanathan, Arya Kumar Bedabrata Chand

Publication date: 30 June 2015

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-014-9882-3

zbMATH Keywords

convergenceparameter identificationpositivityfractalsiterated function systemsrational fractal functions

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Approximation by rational functions (41A20) Interpolation in approximation theory (41A05) Approximation with constraints (41A29) Fractals (28A80) Real rational functions (26C15)

Related Items (12)

A fractal procedure for monotonicity preserving interpolation ⋮ Positivity Preserving Rational Cubic Trigonometric Fractal Interpolation Functions ⋮ Piecewise rational interpolation by witch of Agnesi ⋮ Bivariate shape preserving interpolation: a fractal-classical hybrid approach ⋮ Constrained shape preserving rational cubic fractal interpolation functions ⋮ Shape preserving rational cubic fractal interpolation function ⋮ Fractal perturbation of shaped functions: convergence independent of scaling ⋮ A Novel Approach to Surface Interpolation: Marriage of Coons Technique and Univariate Fractal Functions ⋮ Constrained 2D Data Interpolation Using Rational Cubic Fractal Functions ⋮ BERNSTEIN FRACTAL RATIONAL APPROXIMANTS WITH NO CONDITION ON SCALING VECTORS ⋮ Kantorovich-Bernstein α-fractal function in 𝓛^P spaces ⋮ Energy minimizing associate fractal functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convexity-preserving interpolatory parametric splines of non-uniform polynomial degree
• Fractal polynomial interpolation
• The calculus of fractal interpolation functions
• Positivity-preserving interpolation of positive data by rational cubics
• Fractal functions and interpolation
• Positivity of cubic polynomials on intervals and positive spline interpolation
• Positive interpolation with rational quadratic splines
• A new \(C^2\) rational interpolation based on function values and constrained control of the interpolant curves
• Counterexamples in parameter identification problem of the fractal interpolation functions
• On the parameter identification problem in the plane and the polar fractal interpolation functions
• Curve and surface construction using variable degree polynomial splines
• Natural bicubic spline fractal interpolation
• Smooth fractal interpolation
• FRACTAL GEOMETRY OF FINANCIAL TIME SERIES
• Every Convex Function is Locally Lipschitz
• Subdivision schemes in geometric modelling
• Convexity-Preserving Polynomial Splines of Non-uniform Degree
• Hidden Variable Fractal Interpolation Functions
• CUBIC SPLINE COALESCENCE FRACTAL INTERPOLATION THROUGH MOMENTS
• Convexity-Preserving Piecewise Rational Quartic Interpolation
• Shape Preserving Piecewise Rational Interpolation
• Shape Preserving Interpolation to Convex Data by Rational Functions with Quadratic Numerator and Linear Denominator
• A relation between fractal dimension and Fourier transform – electroencephalographic study using spectral and fractal parameters
• Generalized Cubic Spline Fractal Interpolation Functions
• An Interpolation Curve Using a Spline in Tension

This page was built for publication: A \(\mathcal{C}^{1}\)-rational cubic fractal interpolation function: convergence and associated parameter identification problem