Computational strategies for surface fitting using thin plate spline finite element methods

Kempthorne, Daryl, Turner, Ian W., & Belward, John A. (2013) Computational strategies for surface fitting using thin plate spline finite element methods. ANZIAM Journal, 54, C56-C71.

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Abstract

Thin plate spline finite element methods are used to fit a surface to an irregularly scattered dataset [S. Roberts, M. Hegland, and I. Altas. Approximation of a Thin Plate Spline Smoother using Continuous Piecewise Polynomial Functions. SIAM, 1:208--234, 2003]. The computational bottleneck for this algorithm is the solution of large, ill-conditioned systems of linear equations at each step of a generalised cross validation algorithm. Preconditioning techniques are investigated to accelerate the convergence of the solution of these systems using Krylov subspace methods. The preconditioners under consideration are block diagonal, block triangular and constraint preconditioners [M. Benzi, G. H. Golub, and J. Liesen. Numerical solution of saddle point problems. Acta Numer., 14:1--137, 2005]. The effectiveness of each of these preconditioners is examined on a sample dataset taken from a known surface. From our numerical investigation, constraint preconditioners appear to provide improved convergence for this surface fitting problem compared to block preconditioners.

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ID Code: 75082
Item Type: Journal Article
Refereed: Yes
Keywords: preconditioning, krylov subspace, thin plate splines, surface fitting
ISSN: 1446-1811
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
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Copyright Owner: Copyright 2013 Australian Mathematical Society
Copyright Statement: Copies of this article must not be made otherwise available on the internet; instead link directly to this url for
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Deposited On: 18 Aug 2014 01:59
Last Modified: 20 Oct 2014 18:02

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