Scattered data approximation on the bisphere and application to texture analysis
type: Item
instance of: scholarly article
title: Scattered data approximation on the bisphere and application to texture analysis
zbMATH Open document ID: 1210.65021
author: Daniel Potts
author: Frank Filbir
published in: Mathematical Geosciences
publication date: 2010-11-03T00:00:00Z
review text: The focus of the paper is to obtain an optimal approximation and interpolation on the bisphere from scattered data. First, the authors collect the basic material on the harmonic analysis on the bisphere (Section 2). Next, they explain the basics for computation on the bisphere (Section 3). The main results of the paper are contained in Section 4, where the authors provide the approximation and interpolation of scattered data in their setting: the Marcienkiewicz-Zygmund inequality (Theorem 6), the estimate of the condition number (Corollary 7), an optimal interpolation problem (Theorem 11), an estimate of the condition number for the normal equation (Corollary 12). Section 5 contains some applications, concerning a texture analysis.
reviewed by: Dan Bărbosu
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D18
zbMATH DE Number: 5809625
zbMATH Keywords: approximation by spherical harmonics
zbMATH Keywords: scattered data interpolation
zbMATH Keywords: iterative methods
zbMATH Keywords: texture analysis
zbMATH Keywords: fast Fourier transform
zbMATH Keywords: bisphere Marcienkiewicz-Zygmund inequality
zbMATH Keywords: condition number
zbMATH Keywords: normal equation
MaRDI profile type: Publication
full work available at URL: s11004-010-9298-1
OpenAlex ID: W2094797996
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DOI: 10.1007/S11004-010-9298-1
description: scientific article; zbMATH DE number 5809625