Multivariate approximation by PDE splines
type: Item
instance of: scholarly article
title: Multivariate approximation by PDE splines
zbMATH Open document ID: 1146.65020
author: M. L. Rodríguez
author: M. Pasadas
published in: Journal of Computational and Applied Mathematics
publication date: 2008-07-11T00:00:00Z
review text: Starting from the data point set characterizing a surface and from the elliptic partial differential equation (PDE) that describes a certain physical phenomenon the authors present the approximation method managing the fitting of the data points by least squares and the solution of the PDE. The so-called PDE spline is the solution of a minimization problem in a convex set in a Sobolev space. This solution is obtained using the method of Lagrangian multipliers. The main purpose of this paper is to prove the existence, the uniqueness and the convergence of the solution in question. The authors present an example to illustrate this fitting method employing the finite-difference discretization to solve PDEs numerically.
reviewed by: Jacek Gilewicz
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65D15
zbMATH DE Number: 5300722
zbMATH Keywords: least squares fitting
zbMATH Keywords: elliptic PDE
zbMATH Keywords: surface design
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: j.cam.2007.10.030
OpenAlex ID: W1989740011
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DOI: 10.1016/J.CAM.2007.10.030
description: scientific article; zbMATH DE number 5300722