A Construction of the Best Fractal Approximation

TL;DR

This paper introduces a method for constructing the optimal fractal approximation within the space of bounded functions, focusing on finite-dimensional subspaces built from continuous fractal functions.

Contribution

It presents a novel approach to build finite-dimensional subspaces of bounded functions using continuous fractal functions and finds the best approximation within these spaces.

Findings

Constructed finite-dimensional subspaces of bounded functions.

Proposed a method to find the best approximation of a continuous function.

Established a framework for continuous best fractal approximation.

Abstract

In this paper we present a method for constructing the continuous best fractal approximation in the space of bounded functions. We construct the finite-dimensional subspace of the space of bounded functions whose base consists of the continuous fractal functions, and propose how to find the best approximation of given continuous function by element of the constructed space.