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


  • Daryl Matthew Kempthorne Queensland University of Technology
  • Ian W Turner Queensland University of Technology
  • John A Belward Queensland University of Technology



preconditioning, krylov subspace, thin plate splines, surface fitting


Thin plate spline finite element methods are used to fit a surface to an irregularly scattered dataset. 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. 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. References
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Author Biography

Ian W Turner, Queensland University of Technology

Head of School Science and Engineering Faculty, Mathematical Sciences





Proceedings Computational Techniques and Applications Conference