The author Judith Weintraub and her husband Dan are living in Switzerland. Now a pensioner, she can look back on an extremely eventful and demanding life. A life that she describes in her first book "Winding Roads" almost woodcut-like and with a lot of heart.
Inverse problems need to be solved in order to properly interpret indirect measurements. Often, inverse problems are ill-posed and sensitive to data errors. Therefore one has to incorporate some sort of regularization to reconstruct significant information from the given data. This book presents the main achievements that have emerged in regularization theory over the past 50 years, focusing on linear ill-posed problems and the development of methods that can be applied to them. Some of this material has previously appeared only in journal articles. A Taste of Inverse Problems: Basic Theory and Examples rigorously discusses state-of-the-art inverse problems theory, focusing on numerically relevant aspects and omitting subordinate generalizations;presents diverse real-world applications, important test cases, and possible pitfalls; and treats these applications with the same rigor and depth as the theory.
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.
This book is intended to help advanced undergraduate, graduate, and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues, as well as optimization of program execution speeds. Numerous examples are given throughout the chapters, followed by comprehensive end-of-chapter problems with a more pronounced physics background, while less stress is given to the explanation of individual algorithms. The readers are encouraged to develop a certain amount of skepticism and scrutiny instead of blindly following readily available commercial tools. The second edition has been enriched by a chapter on inverse problems dealing with the solution of integral equations, inverse Sturm-Liouville problems, as well as retrospective and recovery problems for partial differential equations. The revised text now includes an introduction to sparse matrix methods, the solution of matrix equations, and pseudospectra of matrices; it discusses the sparse Fourier, non-uniform Fourier and discrete wavelet transformations, the basics of non-linear regression and the Kolmogorov-Smirnov test; it demonstrates the key concepts in solving stiff differential equations and the asymptotics of Sturm-Liouville eigenvalues and eigenfunctions. Among other updates, it also presents the techniques of state-space reconstruction, methods to calculate the matrix exponential, generate random permutations and compute stable derivatives.
This book takes readers on a tour through modern methods in image analysis and reconstruction based on level set and PDE techniques, the major focus being on morphological and geometric structures in images. The aspects covered include edge-sharpening image reconstruction and denoising, segmentation and shape analysis in images, and image matching. For each, the lecture notes provide insights into the basic analysis of modern variational and PDE-based techniques, as well as computational aspects and applications.
This is one of the first four in a new series of fabulously illustrated natural history travel guides, intended for the general reader with an interest in natural history, and for the growing numbers of 'ecotourists' who want to know where to see wildlife in the countries they visit. Thebooks are designed to complement each other and to build into a nature library, together giving an introduction to the natural history of Europe.Britain's compact scale belies the diversity of its landscapes - from sea-cliffs and rocky offshore islands, to the massifs of the Scottish Highlands, the low fenland of East Anglia, and the gentle wooded coombes of the south-west. This fabulously illustrated new travel guide describes hundreds ofplaces where these landscapes and their inhabitants can be seen at their best, all in easy reach of the discerning traveller.Essentially practical, the book first introduces the ecology, geology, and wildlife of Britain, then goes on to describe where to see its natural history at its best. There are descriptions of a selection of some 200 sites to visit, each carefully chosen to show a range of habitats and fascinatingwildlife. The entries are the personal choice of the authors and are based on intensive travel and research in the region. Described sites range in size from a few to thousands of hectares, be they National Parks, nature reserves, or simply common land, but all are open to the public and accessibleto the ordinary visitor. Four colour throughout, this book has stunning landscape photographs, line drawings and photographs of individual animals of plants and animals, colour region and site maps, and a splendid composite painting encapsulating typical habitats and their inhabitants.
High above the mountaintops on the Isle of Mull, a huge bird is soaring. Its all-encompassing gaze records people in its Hebridean territory far below, but they are of no interest. The eagle is about its business: concentrating on the deer and fidgety hares out grazing in the morning sun, the urgent push of thermals beneath its wings, a threatening weather front way out at sea, and the restless chick back in its eyrie. This is Mull in its glory. This is what the excited, watching people have travelled so far to witness. They train their binoculars and admire, perhaps envy, the eagle with its vast freedom, knowing that such a self-willed being is part of another world – almost. This book guides the reader through that world. With superb illustrations and illuminating text, we are led to the wild side of Mull. Every facet of the island’s natural history is considered, its diverse species and many stories – past, present and future. Along the way we are reminded that wildness is not somehow separate from the human world but influenced, and shared, by nature and people together. Here is the tale of a precious and unique place, a seaborne landscape that displays an uncommon biodiversity and rare wildlife experiences, although today it also faces its greatest challenges. Most of all, this book is testimony to the power of wild places and the duty we have to learn from and protect them.
The conjugate gradient method is a powerful tool for the iterative solution of self-adjoint operator equations in Hilbert space.This volume summarizes and extends the developments of the past decade concerning the applicability of the conjugate gradient method (and some of its variants) to ill posed problems and their regularization. Such problems occur in applications from almost all natural and technical sciences, including astronomical and geophysical imaging, signal analysis, computerized tomography, inverse heat transfer problems, and many more This Research Note presents a unifying analysis of an entire family of conjugate gradient type methods. Most of the results are as yet unpublished, or obscured in the Russian literature. Beginning with the original results by Nemirovskii and others for minimal residual type methods, equally sharp convergence results are then derived with a different technique for the classical Hestenes-Stiefel algorithm. In the final chapter some of these results are extended to selfadjoint indefinite operator equations. The main tool for the analysis is the connection of conjugate gradient type methods to real orthogonal polynomials, and elementary properties of these polynomials. These prerequisites are provided in a first chapter. Applications to image reconstruction and inverse heat transfer problems are pointed out, and exemplarily numerical results are shown for these applications.
The author Judith Weintraub and her husband Dan are living in Switzerland. Now a pensioner, she can look back on an extremely eventful and demanding life. A life that she describes in her first book "Winding Roads" almost woodcut-like and with a lot of heart.
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