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**Investigation of regularized techniques for boundary knot method.**
*(English)*
Zbl 1208.65173

Summary: This study investigates regularization techniques for the boundary knot method (BKM). We consider three regularization methods and two approaches for the determination of the regularization parameter. Our numerical experiments show that Tikhonov regularization in conjunction with generalized cross-validation approach outperforms the other regularization techniques in the BKM solution of Helmholtz and modified Helmholtz problems.

### MSC:

65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |

35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |

65F20 | Numerical solutions to overdetermined systems, pseudoinverses |

### Keywords:

boundary knot method; regularization method; singular value decomposition; Helmholtz problem; numerical experiments; Tikhonov regularization; generalized cross-validation### Software:

Regularization tools
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\textit{F. Wang} et al., Int. J. Numer. Methods Biomed. Eng. 26, No. 12, 1868--1877 (2010; Zbl 1208.65173)

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### References:

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