A review of shape preserving approximation methods and algorithms for approximating univariate functions or discrete data is given. The notion of 'shape' refers to the geometrical behavior of a function's or approximant's graph, and usually includes positivity, monotonicity, and/or convexity. But, in the recent literature, the broader concept of shape also… (More)
In this article we examine the possibility of improving the recursive algorithm for computation of box-dimension of complex sets. The known method of box-counting is simplified down to the simple sign counting operation. Our target set is a "cloud" of amorphous points since many fractal sets are given in this form. The key of the algorithm are affine… (More)
Fluctuation of wind speed affects wind energy systems since the potential wind power is proportional the cube of wind speed. Hence precise prediction of wind speed is very important to improve the performances of the systems. Due to unstable behavior of the wind speed above different terrains, in this study fractal characteristics of the wind speed series… (More)
Nonlinear systems, defined by a system of ODE's, usually contain nonlinear terms. Under some circumstances these terms can be locally approximated by linear factors and by discretization can be transformed in the sequence of (hyperbolic) Iterated Function Systems (IFS). Then, this IFS generate a unique attractor that uses as a kind of characteristic set… (More)
It is known that every hyperbolic Iterated Function System containing affine mappings can be represented in barycentric form by which it becomes affine invariant. Some properties were surveyed and some new ones were established. Examples of fractal sets supplement the theory.