Explicit multivariate approximations from cell-average data

TL;DR

This paper introduces a constructive method for high-order global approximation of smooth multivariate functions using cell-average data, employing B-spline based quasi-interpolation operators derived from univariate cases.

Contribution

It provides a new explicit procedure for high-order approximation from cell-average data and develops univariate B-spline quasi-interpolation operators for this purpose.

Findings

High-order point-value approximations from cell-average data

Development of univariate B-spline quasi-interpolation operators

Multivariate spline approximation via tensor products

Abstract

Given gridded cell-average data of a smooth multivariate function, we present a constructive explicit procedure for generating a high-order global approximation of the function. One contribution is the derivation of high order approximations to point-values of the function directly from the cell-average data. The second contribution is the development of univariate B-spline based high order quasi-interpolation operators using cell-average data. Multivariate spline quasi-interpolation approximation operators are obtained by tensor products of the univariate operators.