Geometric Weakly Admissible Meshes, Discrete Least Squares Approximations and Approximate Fekete Points

TL;DR

This paper introduces a method combining geometric weakly admissible meshes and QR-based algorithms to efficiently compute points for multivariate least squares approximation and interpolation.

Contribution

It presents a novel approach that leverages geometric weakly admissible meshes for improved computation of approximation points.

Findings

Efficient algorithms for multivariate least squares approximation.

Effective computation of approximate Fekete points.

Enhanced interpolation accuracy using the proposed method.

Abstract

Using the concept of Geometric Weakly Admissible Meshes together with an algorithm based on the classical QR factorization of matrices, we compute efficient points for discrete multivariate least squares approximation and Lagrange interpolation.