skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Bicubic partially blended rational fractal surface for a constrained interpolation problem

Abstract

This paper investigates some univariate and bivariate constrained interpolation problems using fractal interpolation functions. First, we obtain rational cubic fractal interpolation functions lying above a prescribed straight line. Using a transfinite interpolation via blending functions, we extend the properties of the univariate rational cubic fractal interpolation function to generate surfaces that lie above a plane. In particular, the constrained bivariate interpolation discussed herein includes a method to construct fractal interpolation surfaces that preserve positivity inherent in a prescribed data set. Uniform convergence of the bivariate fractal interpolant to the original function which generates the data is proven.

Authors:
 [1];  [2];  [3]
  1. Indian Institute of Technology Madras, Department of Mathematics (India)
  2. Indian Institute of Technology Delhi, Department of Mathematics (India)
  3. VIT University, Chennai Campus, Department of Mathematics (India)
Publication Date:
OSTI Identifier:
22769368
Resource Type:
Journal Article
Journal Name:
Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 37; Journal Issue: 1; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CONVERGENCE; FRACTALS; FUNCTIONS; INTERPOLATION; SURFACES

Citation Formats

Chand, A. K. B.,, Viswanathan, P., E-mail: viswa@maths.iitd.ac.in, and Vijender, N., E-mail: vijendernallapu@gmail.com. Bicubic partially blended rational fractal surface for a constrained interpolation problem. United States: N. p., 2018. Web. doi:10.1007/S40314-016-0373-1.
Chand, A. K. B.,, Viswanathan, P., E-mail: viswa@maths.iitd.ac.in, & Vijender, N., E-mail: vijendernallapu@gmail.com. Bicubic partially blended rational fractal surface for a constrained interpolation problem. United States. doi:10.1007/S40314-016-0373-1.
Chand, A. K. B.,, Viswanathan, P., E-mail: viswa@maths.iitd.ac.in, and Vijender, N., E-mail: vijendernallapu@gmail.com. Thu . "Bicubic partially blended rational fractal surface for a constrained interpolation problem". United States. doi:10.1007/S40314-016-0373-1.
@article{osti_22769368,
title = {Bicubic partially blended rational fractal surface for a constrained interpolation problem},
author = {Chand, A. K. B., and Viswanathan, P., E-mail: viswa@maths.iitd.ac.in and Vijender, N., E-mail: vijendernallapu@gmail.com},
abstractNote = {This paper investigates some univariate and bivariate constrained interpolation problems using fractal interpolation functions. First, we obtain rational cubic fractal interpolation functions lying above a prescribed straight line. Using a transfinite interpolation via blending functions, we extend the properties of the univariate rational cubic fractal interpolation function to generate surfaces that lie above a plane. In particular, the constrained bivariate interpolation discussed herein includes a method to construct fractal interpolation surfaces that preserve positivity inherent in a prescribed data set. Uniform convergence of the bivariate fractal interpolant to the original function which generates the data is proven.},
doi = {10.1007/S40314-016-0373-1},
journal = {Computational and Applied Mathematics},
issn = {0101-8205},
number = 1,
volume = 37,
place = {United States},
year = {2018},
month = {3}
}