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Regularization of Inverse Problems
This book is devoted to the mathematical theory of regularization methods and gives an account of the currently available results about regularization methods for linear and nonlinear ill-posed problems. Both continuous and iterative regularization methods are considered in detail with special emphasis on the development of parameter choice and stopping rules which lead to optimal convergence rates.
Numerical Methods for the Solution of Ill-Posed Problems
Many problems in science, technology and engineering are posed in the form of operator equations of the first kind, with the operator and RHS approximately known. But such problems often turn out to be ill-posed, having no solution, or a non-unique solution, and/or an unstable solution. Non-existence and non-uniqueness can usually be overcome by settling for `generalised' solutions, leading to the need to develop regularising algorithms. The theory of ill-posed problems has advanced greatly since A. N. Tikhonov laid its foundations, the Russian original of this book (1990) rapidly becoming a classical monograph on the topic. The present edition has been completely updated to consider linear ill-posed problems with or without a priori constraints (non-negativity, monotonicity, convexity, etc.). Besides the theoretical material, the book also contains a FORTRAN program library. Audience: Postgraduate students of physics, mathematics, chemistry, economics, engineering. Engineers and scientists interested in data processing and the theory of ill-posed problems.
Magnetotellurics in the Context of the Theory of Ill-posed Problems
This volume serves as an introduction to modern magnetotellurics originating with the pioneering work of Tikhonov and Cagniard. It presents a comprehensive summary of theoretical and methodological aspects of magnetotellurics. It provides a bridge between textbooks on electrical prospecting and numerous papers on magnetotelluric methods scattered among various geophysical journals and collections. The book has been written in the terms of the theory of ill-posed problems and contains a special chapter encouraging readers to master the elements of this theory that defines the philosophy of the physical experiment. The book thus offers the connected and consistent account of the principles of ...
Multiscale Potential Theory
This self-contained text/reference provides a basic foundation for practitioners, researchers, and students interested in any of the diverse areas of multiscale (geo)potential theory. New mathematical methods are developed enabling the gravitational potential of a planetary body to be modeled using a continuous flow of observations from land or satellite devices. Harmonic wavelets methods are introduced, as well as fast computational schemes and various numerical test examples. Presented are multiscale approaches for numerous geoscientific problems, including geoidal determination, magnetic field reconstruction, deformation analysis, and density variation modelling With exercises at the end of each chapter, the book may be used as a textbook for graduate-level courses in geomathematics, applied mathematics, and geophysics. The work is also an up-to-date reference text for geoscientists, applied mathematicians, and engineers.
A History of Foreign Students in Britain
Foreign students have travelled to Britain for centuries and, from the beginning, attracted controversy. This book explores changing British policy and practice, and changing student experience, set within the context of British social and political history.
Biomedical EPR - Part A: Free Radicals, Metals, Medicine and Physiology
Biomedical EPR – Part A focuses on applications of EPR spectroscopy in the areas of free radicals, metals, medicine, and physiology. The book celebrates the 70th birthday of Prof. James S. Hyde, Medical College of Wisconsin, and his contributions to this field. Chapters are written to provide introductory material for new-comers to the field which lead into up-to-date reviews that provide perspective on the wide range of questions that can be addressed by EPR. Key Features: Free Radicals in Medicine Radicals in vivo and in Model Systems, and their Study by Spin Trapping In vivo EPR, including Oximetry and Imaging Time Domain EPR at Radio Frequencies EPR of Copper Complexes: Motion and Frequency Dependence Time Domain EPR and Electron Spin Echo Envelope Modulation
Variational Source Conditions and Conditional Stability Estimates for Inverse Problems in PDEs
In inverse problems one wants to find some parameter of interest which is not directly observable by indirect measurement. These measurements are usually noisy while the mapping of measurement to parameter is typically illposed (that is unstable). Therefore one applies regularization techniques that balance these two factors to find a stable approximation of the sought for parameter. However, in order to bound the reconstruction error, one needs additional information on the true parameter, which is nowadays typically formulated in terms of variational source conditions. In this thesis, we develop a general strategy to verify these conditions based on smoothness of the true parameter and the illposedness of the problem; the latter will be characterized by exploiting structural similarities to stability estimates. Following this, we apply our strategy to verify variational source conditions for parameter identification problems, inverse scattering and electrical impedance tomography.
Inverse Problems of Vibrational Spectroscopy
The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
Geoelectromagnetic Investigation of the Earth’s Crust and Mantle
Electrical conductivity is a parameter which characterizes composition and physical state of the Earth's interior. Studies of the state equations of solids at high temperature and pressure indicate that there is a close relation be tween the electrical conductivity of rocks and temperature. Therefore, measurements of deep conductivity can provide knowledge of the present state and temperature of the Earth's crust and upper mantle matter. Infor mation about the temperature of the Earth's interior in the remote past is derived from heat flow data. Experimental investigation of water-containing rocks has revealed a pronounced increase of electrical conductivity in the temperature range D from 5...
