相关论文: Non-linear Fractal Interpolating Functions
In nature, there are many phenomena with both irregularity and uncertainty. Therefore, a fuzzy-valued fractal interpolation is more useful for modeling them than fuzzy interpolation or fractal interpolation. We construct fractal…
We present some work relating to fractal transformations on masked iterated function systems and demonstrate how well known algorithms for generating fractal transformations can be modifed for these systems. We also demonstrate that these…
We present an introduction to fractal interpolation beginning with a global set-up and then extending to a local, a non-stationary, and finally the novel quaternionic setting. Emphasis is placed on the overall perspective with references…
Interpolation of classes of differentiated functions given on a finite interval by trigonometric splines using the phantom node method is considered. This method consists in supplementing a given sequence of values of an approximate…
We construct an example of an iterated function system on the line, consisting of linear fractional transformations, such that two of the maps share a fixed points, but the dimension of the attractor equals the conformal dimension, so that…
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…
We provide a rigorous study on dimensions of fractal interpolation function defined on a closed and bounded interval of $\mathbb{R}$ which is associated to a continuous function with respect to a base function, scaling functions and a…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
By appropriate choices of elements in the underlying iterated function system, methodology of fractal interpolation entitles one to associate a family of continuous self-referential functions with a prescribed real-valued continuous…
This article aims to study fractal interpolation functions corresponding to a sequence of iterated function systems (IFSs). For a suitable choice of a sequence of IFS parameters, the corresponding non-stationary fractal function is a better…
Local iterated function systems are an important generalisation of the standard (global) iterated function systems (IFSs). For a particular class of mappings, their fixed points are the graphs of local fractal functions and these functions…
Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…
Local fractional derivative and integrals are revealed as one of useful tools to deal with everywhere continuous but nowhere differentiable functions in fractal areas ranging from fundamental science to engineering. In this paper, a…
In this article, we investigate partial integrals and partial derivatives of bivariate fractal interpolation functions. We prove also that the mixed Riemann-Liouville fractional integral and derivative of order $\gamma = (p, q); p > 0,q >…
Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated function system (IFS) corresponding to the data set is the graph of the FIF. Coalescence…
A method based on orthogonal function series interpolation of the square root probability density to analyze higher dimensional scattered data is presented. The method is targeted for the use-case when the model and/or data are available…
This paper presents a new approach of constructing $\alpha$-fractal interpolation functions (FIFs) using neural network operators, integrating concepts from approximation theory. Initially, we construct $\alpha$-fractals utilizing neural…
The double-direction orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0,1]with the weighting function 1. Functional and recurrent relations are derived for the sequences…
In this article, we construct the multivariate fractal interpolation functions for a given data points and explore the existence of $\alpha$-fractal function corresponding to the multivariate continuous function defined on $[0,1]\times…
The Fatou-Julia theory for rational functions has been extended both to transcendental meromorphic functions and more recently to several different types of quasiregular mappings in higher dimensions. We extend the iterative theory to…