Approximate global convergence and adaptivity for coefficient inverse problems. Beilina, L. & Klibanov, M., V. Volume 9781441978059 , Springer US, 8, 2012. ![Approximate global convergence and adaptivity for coefficient inverse problems [pdf]](https://bibbase.org/img/filetypes/pdf.svg "pdf")
Paper abstract bibtex © 2012 Springer Science+Business Media, LLC. All rights reserved. Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems is the first book in which two new concepts of numerical solutions of multidimensional Coefficient Inverse Problems (CIPs) for a hyperbolic Partial Differential Equation (PDE) are presented: Approximate Global Convergence and the Adaptive Finite Element Method (adaptivity for brevity). Two central questions for CIPs are addressed: How to obtain a good approximations for the exact solution without any knowledge of a small neighborhood of this solution, and how to refine it given the approximation. The book also combines analytical convergence results with recipes for various numerical implementations of developed algorithms. The developed technique is applied to two types of blind experimental data, which are collected both in a laboratory and in the field. The result for the blind backscattering experimental data collected in the field addresses a real world problem of imaging of shallow explosives.
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abstract = {© 2012 Springer Science+Business Media, LLC. All rights reserved. Approximate Global Convergence and Adaptivity for Coefficient Inverse Problems is the first book in which two new concepts of numerical solutions of multidimensional Coefficient Inverse Problems (CIPs) for a hyperbolic Partial Differential Equation (PDE) are presented: Approximate Global Convergence and the Adaptive Finite Element Method (adaptivity for brevity). Two central questions for CIPs are addressed: How to obtain a good approximations for the exact solution without any knowledge of a small neighborhood of this solution, and how to refine it given the approximation. The book also combines analytical convergence results with recipes for various numerical implementations of developed algorithms. The developed technique is applied to two types of blind experimental data, which are collected both in a laboratory and in the field. The result for the blind backscattering experimental data collected in the field addresses a real world problem of imaging of shallow explosives.},
bibtype = {book},
author = {Beilina, Larisa and Klibanov, Michael Victor}
}
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