Least squares approximation and extremal properties
type: Item
instance of: scholarly article
zbMATH Open document ID: 1248.41022
publication date: 2012-07-02T00:00:00Z
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 42A82
zbMATH DE Number: 6052040
zbMATH Keywords: spline functions
zbMATH Keywords: least squares approximation
zbMATH Keywords: best approximation
zbMATH Keywords: regularization
zbMATH Keywords: conditionally positive definite functions
author: Hans Strauss
MaRDI profile type: Publication
title: Least squares approximation and extremal properties
published in: Jaen Journal on Approximation
review text: This paper deals with best approximation in semi-inner product spaces \(H\) where functions of \(H\) are approximated in the underlying semi-norm by functions of a finite dimensional subspace \(U\). The approximation problems are transformed to quadratic optimization problems. The different regularization terms are used in these approximation problems. The solutions of these best approximations satisfy important extremal properties. The main purpose of the paper is to study such extremal properties. Some results of the paper are well-known. The new results are applied to some special problems. The examples show the meaning of the new results.
reviewed by: V. L. Leontiev
description: scientific article; zbMATH DE number 6052040