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Lin, Ji; Chen, Wen; Wang, Fuzhang

A new investigation into regularization techniques for the method of fundamental solutions. (English) Zbl 1210.65198

Math. Comput. Simul. 81, No. 6, 1144-1152 (2011).
Summary: We examine different regularization approaches to investigate the solution stability of the method of fundamental solutions (MFS). We compare three regularization methods in conjunction with two different regularization parameters to find the optimal stable MFS scheme. Meanwhile, we investigate the relationship among the condition number, the effective condition number, and the MFS solution accuracy. Numerical results show that the damped singular value decomposition under the parameter choice of the generalized cross-validation performs the best in terms of the MFS stability analysis. We also find that the condition number is a superior criterion to the effective condition number.

Cited in 54 Documents

MSC:

65N80 Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65F35 Numerical computation of matrix norms, conditioning, scaling
65F22 Ill-posedness and regularization problems in numerical linear algebra

Keywords:

method of fundamental solutions; regularization technique; regularization parameter; effective condition number; stability; numerical results; singular value decomposition; generalized cross-validation

Software:

SERBA; Regularization tools
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\textit{J. Lin} et al., Math. Comput. Simul. 81, No. 6, 1144--1152 (2011; Zbl 1210.65198)
Full Text: DOI

References:

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