A novel for prediction and approximation of functions (self approximation method)

TL;DR

This paper introduces a new self-approximation method for functions that constructs basis functions from the function itself, demonstrating comparable power to Fourier series and wavelets in natural and financial data prediction.

Contribution

The paper presents a novel self-approximation technique that adapts basis functions from the target function, offering a more natural alternative to traditional methods like Fourier and wavelet series.

Findings

Comparable prediction power to Fourier series and wavelets

More natural basis construction from the function itself

Effective in natural and financial data approximation

Abstract

Throughout this article the major idea and conclusion is about comparing this method with some very famous methods like fourier series and wavelet, to show that the power of this approximation method is as much as to predicate many natural and finance methods, something which we can not say the same for wavelets and Fourier series, since this method consider the function itself to make the base functions, and it is more natural rather than wavelets method and fourier series, which they consider some prior functions as basis.