Hon, Y. C.; Wei, T. Backus-Gilbert algorithm for the Cauchy problem of the Laplace equation. (English) Zbl 0980.35167 Inverse Probl. 17, No. 2, 261-271 (2001). Summary: 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 given based on the Backus-Gilbert algorithm. For numerical verification, several examples which include random noise in the initial Cauchy data are presented. Cited in 56 Documents MSC: 35R25 Ill-posed problems for PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation Keywords:moment problem; numerical approximation; convergence; stability PDFBibTeX XMLCite \textit{Y. C. Hon} and \textit{T. Wei}, Inverse Probl. 17, No. 2, 261--271 (2001; Zbl 0980.35167) Full Text: DOI Link