Backus-Gilbert algorithm for the Cauchy problem of the Laplace equation

In this paper, the highly ill posed Cauchy problem for the Laplace equation is transformed to a classical moment problem whose numerical approximation can be achieved. Proofs on its convergence and stability estimates are giv en based on the Backus-Gilbert algorithm. For numerical verification, sever al examples which include random noise in the initial Cauchy data are prese nted.