A Direct Prediction of the Shape Parameter -- a purely scattered data approach

TL;DR

This paper introduces a new method for directly predicting the optimal shape parameter for multiquadrics and inverse multiquadrics in a scattered data setting, enhancing practical applicability.

Contribution

It presents a novel approach for predicting the shape parameter directly from scattered data, unlike previous methods that relied on evenly spaced data.

Findings

Effective prediction of shape parameter in scattered data scenarios

Improved practical utility over previous evenly spaced data methods

Potential for broader application in scattered data interpolation

Abstract

Unlike the previous papers of the author, which are in an evenly spaced data setting, we present an approach which predicts the optimal value of the shape parameter contained in the muiltiquadrics and inverse multiquadrics in a purely scattered data setting. For the purpose of practical application, this approach is expected to be more useful.