Matrices Associated with Moving Least-Squares Approximation and Corresponding Inequalities

TL;DR

This paper investigates properties of matrices in moving least-squares approximation, using singular-value decomposition and inequalities to establish bounds on the coefficients' norm, contributing to the theoretical understanding of the method.

Contribution

It introduces new inequalities and properties of matrices related to moving least-squares approximation, enhancing theoretical insights into the method.

Findings

Proven properties of matrices in moving least-squares approximation.

Established inequalities for singular-values and coefficient norms.

Provided theoretical bounds relevant to approximation accuracy.

Abstract

In this short article, some properties of matrices of moving least-squares approximation have been proven.The used technique is based on singular-value decomposition and inequalities for singular-values. Some inequalities for the norm of coefficients-vector of the linear approximation have been proven.