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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.
The method of least squares, discovered by Gauss in 1795, is a principal tool for reducing the influence of errors when fitting a mathematical model to given observations. Applications arise in many areas of science and engineering. The increased use of automatic data capturing frequently leads to large-scale least squares problems. Such problems can be solved by using recent developments in preconditioned iterative methods and in sparse QR factorization. The first edition of Numerical Methods for Least Squares Problems was the leading reference on the topic for many years. The updated second edition stands out compared to other books on this subject because it provides an in-depth and up-to...
Petrarch’s revival of the ancient practice of laureation in 1341 led to the laurel being conferred on poets throughout Europe in the later Middle Ages and the Early Modern period. Within the Holy Roman Empire, Maximilian I conferred the title of Imperial Poet Laureate especially frequently, and later it was bestowed with unbridled liberality by Counts Palatine and university rectors too. This handbook identifies more than 1300 poets laureated within the Empire and adjacent territories between 1355 and 1804, giving (wherever possible) a sketch of their lives, a list of their published works, and a note of relevant scholarly literature. The introduction and various indexes provide a detailed account of a now largely forgotten but once significant literary-sociological phenomenon and illuminate literary networks in the Early Modern period. A supplementary Volume 5 of Poets Laureate in the Holy Roman Empire. A Bio-bibliographical Handbook will be published in June 2019.
This expansive volume describes the history of numerical methods proposed for solving linear algebra problems, from antiquity to the present day. The authors focus on methods for linear systems of equations and eigenvalue problems and describe the interplay between numerical methods and the computing tools available at the time. The second part of the book consists of 78 biographies of important contributors to the field. A Journey through the History of Numerical Linear Algebra will be of special interest to applied mathematicians, especially researchers in numerical linear algebra, people involved in scientific computing, and historians of mathematics.
The aim of this book is to reflect on the complex practice of responsibility within the context of a globalised world and contemporary means of action. Levinas' exploration of the ethical serves as point of entry and is shown to be seeking inter-cultural political relevance through engagement with the issues of postcoloniality and humanism. Yet, Levinas fails to realise the ethical implications of the inevitable instrumental mediation between ethical meaning and political practice. With recourse to Weber, Apel and Ricoeur, Ernst Wolff proposes a theory of strategic co-responsibility for the uncertain global context of practice.
This volume, by offering a score of new insights derived from a wide variety of recent archaeological and textual sources, bring to life an important overseas trading port in Southeast Asia: Quanzhou. During the Song and Yuan dynasties active official and unofficial engagement in trade had formative effects on the development of the maritime trade of Quanzhou and its social and economic position both regionally and supraregionally. In the first part subjects such as the impact of the Song imperial clan and the local élites on these developments, the economic importance of metals, coins, paper money, and changes in the political economy, are amply discussed. The second part concentrates on the quantitative and qualitative analysis of archaeological data and materials, the investigation of commodities from China, their origins, distribution and final destinations, the use of foreign labour, and the particular role of South Thailand in trade connections, thus supplying the hard data underlying the main argument of the book.