A Qualitative Approach to Inverse Scattering Theory, Fioralba Cakoni; David Colton

Автор: Colton
Название: Integral Equation Methods in Inverse Scattering Theory
ISBN: 1611973155 ISBN-13(EAN): 9781611973150
Издательство: Mare Nostrum (Eurospan)
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Цена: 97950.00 T
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Описание: Scattering theory, a powerful method for the analysis of PDEs, represents one of the most important developments in mathematical physics of recent decades. This classic book is ideal as a supplemental text in a graduate course on scattering theory or inverse problems, and will also be of interest to research scientists in mathematics, physics and engineering. The exposition is based on a rigorous treatment of the Riesz–Fredholm theory of compact operators in dual systems, followed by a derivation of the jump conditions and mapping properties of scalar and vector potentials in spaces of continuous functions. These results are then used to study scattering problems for the Helmholtz and Maxwell equations. The reader will find an in-depth treatment of the use of boundary integral equations to solve scattering problems for acoustic and electromagnetic waves, and an introduction to inverse scattering theory with an emphasis on a function-theoretic approach.

Автор: Isakov V.
Название: Inverse Problems for Partial Differential Equations
ISBN: 0387253645 ISBN-13(EAN): 9780387253640
Издательство: Springer
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Цена: 93160.00 T
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Описание: The topic of the inverse problems is of substantial and rapidly growing interest for many scientists and engineers. The second edition covers most important recent developments in the field of inverse problems, describing theoretical and computational methods, and emphasizing new ideas and techniques. It also reflects new changes since the first edition, including some corrections. This edition is considerably expanded, with some concepts such as pseudo-convexity, and proofs simplified. New material is added to reflect recent progress in theory of inverse problems.This book is intended for mathematicians working with partial differential equations and their applications, and physicists, geophysicists and engineers involved with experiments in nondestructive evaluation, seismic exploration, remote sensing and tomography.

Автор: Eric Gautier and Pierre Alquier
Название: Inverse problems and high-dimensional estimation
ISBN: 3642199887 ISBN-13(EAN): 9783642199882
Издательство: Springer
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Цена: 102480.00 T
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Описание: The product of a high-flying summer school in Paris in 2009, this volume synthesises the state of the art on ill-posed statistical inverse problems and high-dimensional estimation and explores the ways these techniques can be applied to economics.

Автор: Ito Kazufumi, Jin Bangti
Название: Inverse Problems: Tikhonov Theory and Algorithms
ISBN: 9814596191 ISBN-13(EAN): 9789814596190
Издательство: World Scientific Publishing
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Цена: 118270.00 T
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Описание:

Inverse problems arise in practical applications whenever one needs to deduce unknowns from observables. This monograph is a valuable contribution to the highly topical field of computational inverse problems. Both mathematical theory and numerical algorithms for model-based inverse problems are discussed in detail. The mathematical theory focuses on nonsmooth Tikhonov regularization for linear and nonlinear inverse problems. The computational methods include nonsmooth optimization algorithms, direct inversion methods and uncertainty quantification via Bayesian inference.

The book offers a comprehensive treatment of modern techniques, and seamlessly blends regularization theory with computational methods, which is essential for developing accurate and efficient inversion algorithms for many practical inverse problems.

It demonstrates many current developments in the field of computational inversion, such as value function calculus, augmented Tikhonov regularization, multi-parameter Tikhonov regularization, semismooth Newton method, direct sampling method, uncertainty quantification and approximate Bayesian inference. It is written for graduate students and researchers in mathematics, natural science and engineering.

Автор: Kirsch, Andreas
Название: Introduction to the mathematical theory of inverse problems
ISBN: 1461428513 ISBN-13(EAN): 9781461428510
Издательство: Springer
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Цена: 74490.00 T
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Описание: This book introduces the area of inverse problems. It examines basic notions and difficulties encountered with ill-posed problems and presents two special nonlinear inverse problems in detail: the inverse spectral problem and the inverse scattering problem.