# 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:

- Indian Institute of Technology Madras, Department of Mathematics (India)
- Indian Institute of Technology Delhi, Department of Mathematics (India)
- 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}

}

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