A New Fast Iterative Method for Interpolation of Multivariate Scattered Data

Abstract: This paper presents Iterative Scalable Smoothing (ISS), a new itera- tive multi-scale method for multivariate interpolation of scattered data. Each iteration step in the process reduces the residues of the current interpolation result by appli- cation of a smoothing operator to a piecewise constant function that interpolates the residues of the current interpolant, and by adding the resulting function to the current approximation, which is initially set to zero. The convergence of the method is proved and conditions for the di®erentiability of the convergence result are given. For a uni- form mesh an e±cient algorithm is constructed, for which the numerical complexity is estimated. Several 2D numerical examples illustrate the theoretical results. By a 3D test with several test-functions and random nodes it is shown that the accuracy of the proposed method is comparable with the quadratic modiffcation of Shepard's method, which is known to be more accurate than triangle-based methods. Then, in 1D tests, by stochastic simulation with random nodes and random functions the ISS method is compared with the Cubic Splines method, Shepard's method and the Kriging method. We also compare the stability of these methods with respect to noisy data. For the special case of regular nodes, properties of the method are verified by comparing its 1D response function with the response function of the cubic spline and the perfect interpolator (the sinc-function). Special attention is paid to the e®ect of the tuning parameter

Angaben zum Objekt

• Standort: Deutsche Nationalbibliothek Frankfurt am Main
• Umfang: Online-Ressource
• Sprache: Englisch

Verweise und Beziehungen

• Erschienen in: A New Fast Iterative Method for Interpolation of Multivariate Scattered Data ; volume:5 ; number:3 ; year:2005 ; pages:276-293 ; Computational methods in applied mathematics ; 5, Heft 3 (2005), 276-293

Beteiligte, Orts- und Zeitangaben

• Urheber: Masjukov, Andrey V. ; Masjukov, Vladimir I.

Weitere Informationen

• DOI: 10.2478/cmam-2005-0014
• URN: urn:nbn:de:101:1-2410261619508.258913274811
• Rechteinformation: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Letzte Aktualisierung: 15.08.2025, 14:32 MESZ