Variation and Minkowski dimension of fractal interpolation surface

The fractal interpolation surface on the rectangular domain is discussed in this paper. We study the properties of the oscillation and the variation of bivariate continuous functions. Then we discuss the special properties of bivariate fractal interpolation function, and estimate the value of its va...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical analysis and applications 2008-09, Vol.345 (1), p.322-334
Main Author: Feng, Zhigang
Format: Article
Language:English
Subjects:
Approximations and expansions
Bivariate continuous function
Exact sciences and technology
Fractal interpolation surface
Geometry
Iterated function system
Mathematical analysis
Mathematics
Measure and integration
Minkowski dimension
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Sciences and techniques of general use
Variation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The fractal interpolation surface on the rectangular domain is discussed in this paper. We study the properties of the oscillation and the variation of bivariate continuous functions. Then we discuss the special properties of bivariate fractal interpolation function, and estimate the value of its variation. Using the relation between the Minkowski dimension of the graph of continuous function and its variation, we obtain the exact value of the Minkowski dimension of the fractal interpolation surface.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2008.03.075