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Related papers: Super Fractal Interpolation Functions

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This contribution introduces a novel signal extrapolation algorithm and its application to image error concealment. The signal extrapolation is carried out by iteratively generating a model of the signal suffering from distortion. Thereby,…

Image and Video Processing · Electrical Eng. & Systems 2022-07-15 Jürgen Seiler , André Kaup

We consider a construction of recurrent fractal interpolation surfaces with function vertical scaling factors and estimation of their box-counting dimension. A recurrent fractal interpolation surface (RFIS) is an attractor of a recurrent…

Dynamical Systems · Mathematics 2013-07-12 Chol-Hui Yun , Hui-Chol Choi , Hyong-Chol O

A \emph{fractal} is an object exhibiting complexity at arbitrarily small scales. In order to study and characterise fractals, one is often interested in quantifying how they fill up space on small scales. This gives rise to various notions…

Classical Analysis and ODEs · Mathematics 2026-03-12 Jonathan M. Fraser

This paper addresses the problem of approximating a function of bounded variation from its scattered data. Radial basis function(RBF) interpolation methods are known to approximate only functions in their native spaces, and to date, there…

Numerical Analysis · Mathematics 2025-12-23 Rajesh Dachiraju

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…

Dynamical Systems · Mathematics 2015-05-20 P. Viswanathan , M. A. Navascues

This paper introduces Fourier duality for a class of affine iterated function systems (IFS) T_i. These systems are determined by a finite family of contractive affine maps in R^d. Our Fourier duality applies to the resulting probability…

Functional Analysis · Mathematics 2007-05-23 Palle E. T. Jorgensen , Steen Pedersen

In the first section we review recent results on the harmonic analysis of fractals generated by iterated function systems with emphasis on spectral duality. Classical harmonic analysis is typically based on groups whereas the fractals are…

Classical Analysis and ODEs · Mathematics 2007-05-23 Palle E. T. Jorgensen , Steen Pedersen

Recently, in [Electronic Transaction on Numerical Analysis, 41 (2014), pp. 420-442] authors introduced a new class of rational cubic fractal interpolation functions with linear denominators via fractal perturbation of traditional…

Numerical Analysis · Mathematics 2016-01-20 A. K. B. Chand , P. Viswanathan , K. M. Reddy

Iterated functions system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on an initial point. In an analogous way, we define a quantum iterated functions system (QIFS), where functions act…

Quantum Physics · Physics 2009-11-07 Artur Lozinski , Karol Zyczkowski , Wojciech Slomczynski

Deterministic and random fractals, within the framework of Iterated Function Systems, have been used to model and study a wide range of phenomena across many areas of science and technology. However, for many applications deterministic…

Probability · Mathematics 2016-08-16 Michael Barnsley , John E. Hutchinson , Örjan Stenflo

The fundamental aim of this paper is to provide the approximation and numerical integration of a discrete set of data points with Bernstein fractal approach. Using Bernstein polynomials in the iterated function system, the paper initially…

General Mathematics · Mathematics 2024-02-09 Aparna M. P. , P. Paramanathan

A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system(RIFS) with function scaling factors and estimate their box-counting…

Dynamical Systems · Mathematics 2014-08-13 Chol-hui Yun , Hyong-chol O. , Hui-chol Choi

In this paper we talk about the so-called SuperMathematics Functions (SMF), which often constiture the base for generating technical neo-geometrical objects.

General Mathematics · Mathematics 2009-03-10 Mircea Eugen Selariu , Marian Nitu , Florentin Smarandache

This paper presents an innovative set of tools to support a methodology for the multichannel interpolation (MCI) of a discrete signal. It is shown that a bandlimited signal $f$ can be exactly reconstructed from finite samples of $g_k$…

Information Theory · Computer Science 2019-04-12 Dong Cheng , Kit Ian Kou

In this paper, we study errors on perturbation of function contractivity factors and box-counting dimension of hidden variable recurrent fractal interpolation function (HVRFIF). The HVRFIF is a hidden variable fractal interpolation function…

Dynamical Systems · Mathematics 2019-06-05 Mi-Kyong Ri , Chol-Hui Yun

Basing on invariant properties of universal multifractals we propose a simple algorithm for interpolation of multifractal densities. The algorithm admits generalization to a multidimensional case. Analitically obtained are multifractal…

chao-dyn · Physics 2007-05-23 V. G. Bar'yahtar , V. Yu. Gonchar , D. Schertzer , V. V. Yanovsky

This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with…

Metric Geometry · Mathematics 2020-10-20 Yann Lanoiselee , Laurent Nivanen , Aziz El Kaabouchi , Qiuping A. Wang

We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…

Dynamical Systems · Mathematics 2008-02-04 Michael Barnsley , John E. Hutchinson , Örjan Stenflo

Single-molecule force spectroscopy (smFS) is a powerful approach to studying molecular self-organization. However, the coupling of the molecule with the ever-present experimental device introduces artifacts, that complicates the…

Chemical Physics · Physics 2023-04-25 Lars Dingeldein , Pilar Cossio , Roberto Covino

Our companion paper \cite{Stojnicnflgscompyx23} introduced a very powerful \emph{fully lifted} (fl) statistical interpolating/comparison mechanism for bilinearly indexed random processes. Here, we present a particular realization of such fl…

Probability · Mathematics 2023-12-01 Mihailo Stojnic