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Journals / Mathematical and Computational Applications / 2010 / Cilt: 15 - Sayı: 5

A generalized cross validation method for the inverse problem of 3-D Maxwell’s equation

Liang DING
Bo HAN
Jiaqi LİU
Pages
784–789
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The results of numerical simulation testify that this method is efficient.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The inverse problem of estimation of the electrical conductivity in the Maxwell’s equation is considered, which is reformulated as a nonlinear equation.
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Key Findings & Data:GCV method decreases the computational expense and overcomes the influence of nonlinearity and ill-posedness.
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Conclusion & Impact:The results of numerical simulation testify that this method is efficient.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

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.

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Cite This Article

DING, L., HAN, B., LİU, J. (2010). A generalized cross validation method for the inverse problem of 3-D Maxwell’s equation. Mathematical and Computational Applications, Cilt: 15 - Sayı: 5, 784–789. https://ajindex.com/articles/279966

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