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Approximate Moving Least-Squares Approximation with Compactly Supported Radial Weights

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Meshfree Methods for Partial Differential Equations

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 26))

Abstract

We use Maz’ya and Schmidt’s theory of approximate approximation to devise a fast and accurate approximate moving least-squares approximation method which does not require the solution of any linear systems. Since we use compactly supported weight functions, the remaining summation is also efficient. We compare our new algorithm with three other approximation methods based on compactly supported radial functions: multilevel interpolation, the standard moving least-squares approximation method, and a multilevel moving least-squares algorithm. A multilevel approximate moving least-squares approximation algorithm is also included.

Supported by the National Science Foundation under grant DMS-0073636

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL, USA

    Gregory E. Fasshauer

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  1. Gregory E. Fasshauer
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Editor information

Editors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Bonn, Wegelerstraße 6, 53115, Bonn, Germany

    Michael Griebel  & Marc Alexander Schweitzer  & 

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Fasshauer, G.E. (2003). Approximate Moving Least-Squares Approximation with Compactly Supported Radial Weights. In: Griebel, M., Schweitzer, M.A. (eds) Meshfree Methods for Partial Differential Equations. Lecture Notes in Computational Science and Engineering, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56103-0_8

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  • DOI: https://doi.org/10.1007/978-3-642-56103-0_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43891-5

  • Online ISBN: 978-3-642-56103-0

  • eBook Packages: Springer Book Archive

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