Variation and Minkowski dimension of fractal interpolation surface

被引：54
作者：
Feng, Zhigang [1 ,2 ]
机构：
[1] Jiangsu Univ, Fac Sci, Zhenjiang 212013, Jiangsu, Peoples R China
[2] Cardiff Univ, Sch Engn, Cardiff CF24 3AA, S Glam, Wales
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2008年 / 345卷 / 01期
关键词：
bivariate continuous function; variation; iterated function system; fractal interpolation surface; Minkowski dimension;
D O I：
10.1016/j.jmaa.2008.03.075
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. (C) 2008 Elsevier Inc. All rights reserved.
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页码：322 / 334
页数：13
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