A weighted least squares method for scattered data fitting
type: Item
instance of: scholarly article
title: A weighted least squares method for scattered data fitting
zbMATH Open document ID: 1140.65019
author: Tianhe Zhou
author: Danfu Han
published in: Journal of Computational and Applied Mathematics
publication date: 2008-06-19T00:00:00Z
review text: The authors present a weighted least squares method in order to find a smooth surface which approximately produces a given set of scattered data points in \(\mathbb{R}^3\). The data are assumed to be contaminated by noise. When the data are reliable, the corresponding weight is 1: when the data are not reliable, the weight (smaller than 1, e.g. \(0.1, 0.01,\dots\)) is chosen according to the size of the noise. Existence and uniqueness of a solution are discussed and an error bound is derived. Some numerical experiments illustrate the performance of the method, which in case of noisy data gives better results than the traditional least squares method.
reviewed by: Delfina Roux
Mathematics Subject Classification ID: 65D10
zbMATH DE Number: 5290874
zbMATH Keywords: weighted least squares method
zbMATH Keywords: Bernstein-Bezier representation of spline
zbMATH Keywords: scattered noisy data
MaRDI profile type: Publication
full work available at URL: j.cam.2007.06.015
OpenAlex ID: W1981467282
cites work: On stable local bases for bivariate polynomial spline spaces
cites work: Bounds on projections onto bivariate polynomial spline spaces with stable local bases
cites work: On the approximation power of bivariate splines
DOI: 10.1016/J.CAM.2007.06.015
description: scientific article; zbMATH DE number 5290874