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    An iterative MFS algorithm for the Cauchy problem associated with the Laplace equation

    Liviu Marin1

    CMES-Computer Modeling in Engineering & Sciences, Vol.48, No.2, pp. 121-154, 2009, DOI:10.3970/cmes.2009.048.121

    Abstract We investigate the numerical implementation of the alternating iterative algorithm originally proposed by ` 12 ` 12 `$12 `&12 `#12 `^12 `_12 `%12 `~12 *Kozlov91 in the case of the Cauchy problem for the two-dimensional Laplace equation using a meshless method. The two mixed, well-posed and direct problems corresponding to every iteration of the numerical procedure are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method. For each direct problem considered, the optimal value of the regularization parameter is chosen according to the generalized cross-validation (GCV) criterion. An efficient More >

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