Two regularization methods for a Cauchy problem for the Laplace equation

By Zhi Qian, C. Fu, Zhenping Li. 2008

85 citations recorded by the source corpus.

Abstract A Cauchy problem for the Laplace equation in a rectangle is considered. Cauchy data are given for y = 0 , and boundary data are for x = 0 and x = π . The solution for 0 y ⩽ 1 is sought. We propose two different regularization methods on the ill-posed problem based on separation of variables. Both methods are applied to formulate regularized solutions which are stably convergent to the exact one with explicit error estimates.

Subfields: Computational Theory and Mathematics, Computer Vision and Pattern Recognition, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a4e71071bdd055e8b8b9533758830f9e2728f221

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In Computational Theory and Mathematics

In Computer Vision and Pattern Recognition

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Citations in the corpus

Numerical solution of the Laplacian Cauchy problem by using a better postconditioning collocation Trefftz method (2013, background): “, the Tikhonov regularization, conditioning by a suitable preconditioner, and truncated singular value decomposition (SVD), are required [3,12,13].”
Two regularization methods for the Cauchy problems of the Helmholtz equation (2010, methodology): “In this paper, we use two regularization methods, a modified Tikhonov regularization method which was also used to solve the inverse heat conduction problem [20], and a truncation method which was also used to solve the inverse heat conduction problem [21], the source identification problem [22] and”