New Approach to Fractal Approximation of Vector-Functions

Konstantin Igudesman,Marsel Davletbaev,Gleb Shabernev

doi:10.1155/2015/278313

Abstract

This paper introduces new approach to approximation of continuous vector-functions and vector sequences by fractal interpolation vector-functions which are multidimensional generalization of fractal interpolation functions. Best values of fractal interpolation vector-functions parameters are found. We give schemes of approximation of some sets of data and consider examples of approximation of smooth curves with different conditions.

Highlights

It is well known that interpolation and approximation are an important tool for interpretation of some complicated data
Still it should be noted that all these conventional nonrecursive methods produce interpolants that are differentiable a number of times except possibly at a finite set of points
In many situations, we deal with irregular forms, which can not be approximate with desired precision

Summary

Introduction

It is well known that interpolation and approximation are an important tool for interpretation of some complicated data. There are multitudes of interpolation methods using several families of functions: polynomial, exponential, rational, trigonometric, and splines to name a few. Fractal approximation became a suitable tool for that purpose. This tool was developed and studied in [1,2,3]. We use fractal interpolation curves [1] and their generalizations [4] instead of canonical smooth functions (polynomials and splines).

Fractal Interpolation Vector-Functions

Approximation

Discretization and Results

Conclusion