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

By Yiu Chung Benny Hon, Ting Wei. 2001

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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 given based on the Backus-Gilbert algorithm. For numerical verification, several examples which include random noise in the initial Cauchy data are presented.

Subfields: Finance, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f6aacede787d7899b7d091a5c990a1d95573719a