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Computation for MultiDimensional Cauchy Problem

This paper devises a computational method for solving a Cauchy problem of Laplace's equation in multidimensional space. By using the Green formula, the Cauchy problem is transformed to a moment problem so that numerical computations using a regularization technique can be achieved. A stability estimation and a suitable choice of regularization parameter for the proposed method are also given. For numerical verification, a numerical example in the three-dimensional case is presented.