Non-local approximation of continuous functions using scattered translates of the general multiquadric $(x^2+c^2)^{k-1/2}$

TL;DR

This paper demonstrates that continuous functions on a closed interval can be approximated arbitrarily well using scattered translates of the general multiquadric function, expanding approximation techniques.

Contribution

It introduces a novel approximation method employing scattered translates of the general multiquadric for continuous functions on closed intervals.

Findings

Continuous functions can be approximated arbitrarily closely.

Scattered translates of the multiquadric are effective for approximation.

The method extends existing approximation theories.

Abstract

This article shows that on a closed interval $[a,b]$ a continuous function may be approximated to an arbitrary degree of accuracy using scattered translates of the general multiquadric $(x^2+c^2)^{k-1/2}$.