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Math. Comput. Appl. 2010, 15(5), 784-789; doi:10.3390/mca15050784

A Generalized Cross Validation Method for the Inverse Problem of 3-D Maxwell's Equation

Department of Mathematics, Harbin Institute of Technology, 150001 Harbin, P. R. China
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Received: 31 December 2010 / Accepted: 31 December 2010 / Published: 31 December 2010
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Abstract

The inverse problem of estimation of the electrical conductivity in the Maxwell’s equation is considered, which is reformulated as a nonlinear equation. The Generalized Cross Validation is used to estimate the global regularization parameter and the damped Gauss-Newton is applied to impose local regularization. The damped Gauss-Newton method requires no calculation of the Hessian matrix which is expensive for traditional Newton method. GCV method decreases the computational expense and overcomes the influence of nonlinearity and ill-posedness. The results of numerical simulation testify that this method is efficient.
Keywords: Maxwell’s Equation; Nonlinear; Ill-posed, Inversion; Damped Gauss-Newton; GCV Maxwell’s Equation; Nonlinear; Ill-posed, Inversion; Damped Gauss-Newton; GCV
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Ding, L.; Han, B.; Liu, J. A Generalized Cross Validation Method for the Inverse Problem of 3-D Maxwell's Equation. Math. Comput. Appl. 2010, 15, 784-789.

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