Multiresolution methods in scattered data modelling.
type: Item
instance of: scholarly article
title: Multiresolution methods in scattered data modelling.
zbMATH Open document ID: 1057.65004
DOI: 10.1007/978-3-642-18754-4
author: Armin Iske
published in: Lecture Notes in Computational Science and Engineering
publication date: 2004-09-29T00:00:00Z
review text: This research monograph concerns the design of efficient, robust and reliable algorithms for the numerical simulation of multiscale phenomena with orientation for applications. Various modern techniques from scattered data modeling, such as splines over triangulation and radial basis functions, are combined with customized adaptive strategies, which are developed individually in this work. Very recent results concerning the approximation order and the numerical stability of polyharmonic spline interpolation [see \textit{J. Duchon}, R.A.I.R.O. Anal. Numér. 12, 325--334 (1978; Zbl 0403.41003)] are renewed. Recent developments concerning thinning algorithms with emphasis on their application to terrain modeling and image compression are given various alternative multilevel approximation methods for bivariate scattered date are also presented [see \textit{M. S. Floater} and \textit{A. Iske}, J. Comput. Appl. Math 73, No.1--2, 65--78 (1996; Zbl 0859.65006)]. Extensive numerical examples, mainly arising from real world application are given. Meshfree recent methods, which are discretization schemes for partial differential equation are also discussed. Special emphasis is given to a comparison between the various numerical algorithms developed here and comparable state-of-the-art methods.
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 68U10
Mathematics Subject Classification ID: 94A08
Mathematics Subject Classification ID: 65-02
Mathematics Subject Classification ID: 65T60
zbMATH DE Number: 2104348
zbMATH Keywords: spline
zbMATH Keywords: radial basis function
zbMATH Keywords: multiresolution methods
zbMATH Keywords: textbook
zbMATH Keywords: scattered data modeling
zbMATH Keywords: triangulation
zbMATH Keywords: approximation order
zbMATH Keywords: numerical stability
zbMATH Keywords: polyharmonic spline interpolation
zbMATH Keywords: thinning algorithms
zbMATH Keywords: terrain modeling
zbMATH Keywords: image compression
zbMATH Keywords: numerical examples
reviewed by: H. P. Dikshit
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-642-18754-4
OpenAlex ID: W1589534817
description: scientific article; zbMATH DE number 2104348