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Least squares collocation solution of elliptic problems in general regions

Author

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  • Pereyra, V.
  • Scherer, G.

Abstract

We consider the solution of elliptic problems in general regions by embedding and least squares approximation of overdetermined collocated tensor product of basis functions. The resulting least squares problem will generally be ill-conditioned or even singular, and thus, regularization techniques are required. Large scale problems are solved by either conjugate gradient type methods or by a block Gauss–Seidel approach. Numerical results are presented that show the viability of the new method.

Suggested Citation

  • Pereyra, V. & Scherer, G., 2006. "Least squares collocation solution of elliptic problems in general regions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(1), pages 226-230.
    • Handle: RePEc:eee:matcom:v:73:y:2006:i:1:p:226-230
    DOI: 10.1016/j.matcom.2006.06.022
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    Cited by:

    1. H. Alwardi & S. Wang & L. Jennings & S. Richardson, 2012. "An adaptive least-squares collocation radial basis function method for the HJB equation," Journal of Global Optimization, Springer, vol. 52(2), pages 305-322, February.
    2. H. Alwardi & S. Wang & L. Jennings, 2013. "An adaptive domain decomposition method for the Hamilton–Jacobi–Bellman equation," Journal of Global Optimization, Springer, vol. 56(4), pages 1361-1373, August.

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