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Surveys On Solution Methods For Inverse Problems
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Book Synopsis Surveys on Solution Methods for Inverse Problems by : David Colton
Download or read book Surveys on Solution Methods for Inverse Problems written by David Colton and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems are concerned with determining causes for observed or desired effects. Problems of this type appear in many application fields both in science and in engineering. The mathematical modelling of inverse problems usually leads to ill-posed problems, i.e., problems where solutions need not exist, need not be unique or may depend discontinuously on the data. For this reason, numerical methods for solving inverse problems are especially difficult, special methods have to be developed which are known under the term "regularization methods". This volume contains twelve survey papers about solution methods for inverse and ill-posed problems and about their application to specific types of inverse problems, e.g., in scattering theory, in tomography and medical applications, in geophysics and in image processing. The papers have been written by leading experts in the field and provide an up-to-date account of solution methods for inverse problems.
Book Synopsis Perspectives on Enclosure Methods by : Ulrich Kulisch
Download or read book Perspectives on Enclosure Methods written by Ulrich Kulisch and published by Springer Science & Business Media. This book was released on 2001-06-18 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Enclosure methods and their applications have been developed to a high standard during the last decades. These methods guarantee the validity of the computed results. This means they are of the same standard as the rest of mathematics. The book deals with a wide variety of aspects of enclosure methods. All contributions follow the common goal to push the limits of enclosure methods forward. Topics that are treated include basic questions of arithmetic, proving conjectures, bounds for Krylow type linear system solvers, bounds for eigenvalues, the wrapping effect, algorithmic differencing, differential equations, finite element methods, application in robotics, and nonsmooth global optimization.
Book Synopsis Computational Methods for Inverse Problems by : Curtis R. Vogel
Download or read book Computational Methods for Inverse Problems written by Curtis R. Vogel and published by SIAM. This book was released on 2002-01-01 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
Book Synopsis Multidisciplinary Methods for Analysis, Optimization and Control of Complex Systems by : Vincenzo Capasso
Download or read book Multidisciplinary Methods for Analysis, Optimization and Control of Complex Systems written by Vincenzo Capasso and published by Springer Science & Business Media. This book was released on 2006-01-05 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of lecture notes of a summer school named after the late Jacques Louis Lions. The summer school was designed to alert both Academia and Industry to the increasing role of multidisciplinary methods and tools for the design of complex products in various areas of socio-economic interest. This volume offers the reader a rare opportunity of being exposed to the presentation of real industrial and societal problems together with the relevant innovative methods used.
Book Synopsis Inverse Problems in the Mathematical Sciences by : Charles W. Groetsch
Download or read book Inverse Problems in the Mathematical Sciences written by Charles W. Groetsch and published by Springer Science & Business Media. This book was released on 2013-12-14 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems are immensely important in modern science and technology. However, the broad mathematical issues raised by inverse problems receive scant attention in the university curriculum. This book aims to remedy this state of affairs by supplying an accessible introduction, at a modest mathematical level, to the alluring field of inverse problems. Many models of inverse problems from science and engineering are dealt with and nearly a hundred exercises, of varying difficulty, involving mathematical analysis, numerical treatment, or modelling of inverse problems, are provided. The main themes of the book are: causation problem modeled as integral equations; model identification problems, posed as coefficient determination problems in differential equations; the functional analytic framework for inverse problems; and a survey of the principal numerical methods for inverse problems. An extensive annotated bibliography furnishes leads on the history of inverse problems and a guide to the frontiers of current research.
Book Synopsis Inverse Problems, Image Analysis, and Medical Imaging by : M. Zuhair Nashed
Download or read book Inverse Problems, Image Analysis, and Medical Imaging written by M. Zuhair Nashed and published by American Mathematical Soc.. This book was released on 2002 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the Special Session, Interaction of Inverse Problems and Image Analysis, held at the January 2001 meeting of the AMS in New Orleans, LA. The common thread among inverse problems, signal analysis, and image analysis is a canonical problem: recovering an object (function, signal, picture) from partial or indirect information about the object. Both inverse problems and imaging science have emerged in recent years as interdisciplinary research fields with profound applications in many areas of science, engineering, technology, and medicine. Research in inverse problems and image processing shows rich interaction with several areas of mathematics and strong links to signal processing, variational problems, applied harmonic analysis, and computational mathematics. This volume contains carefully referred and edited original research papers and high-level survey papers that provide overview and perspective on the interaction of inverse problems, image analysis, and medical imaging. The book is suitable for graduate students and researchers interested in signal and image processing and medical imaging.
Book Synopsis Regularization Methods in Banach Spaces by : Thomas Schuster
Download or read book Regularization Methods in Banach Spaces written by Thomas Schuster and published by Walter de Gruyter. This book was released on 2012-07-30 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of applications ranging from medical imaging and non-destructive testing via finance to systems biology. Many of these problems belong to the class of parameter identification problems in partial differential equations (PDEs) and thus are computationally demanding and mathematically challenging. Hence there is a substantial need for stable and efficient solvers for this kind of problems as well as for a rigorous convergence analysis of these methods. This monograph consists of five parts. Part I motivates the importance of developing and analyzing regularization methods in Banach spaces by presenting four applications which intrinsically demand for a Banach space setting and giving a brief glimpse of sparsity constraints. Part II summarizes all mathematical tools that are necessary to carry out an analysis in Banach spaces. Part III represents the current state-of-the-art concerning Tikhonov regularization in Banach spaces. Part IV about iterative regularization methods is concerned with linear operator equations and the iterative solution of nonlinear operator equations by gradient type methods and the iteratively regularized Gauß-Newton method. Part V finally outlines the method of approximate inverse which is based on the efficient evaluation of the measured data with reconstruction kernels.
Book Synopsis Inverse Problems in Vibration by : G.M.L. Gladwell
Download or read book Inverse Problems in Vibration written by G.M.L. Gladwell and published by Springer Science & Business Media. This book was released on 2004-08-10 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first, 1986, edition of this book, inverse problems in vibration were interpreted strictly: problems concerning the reconstruction of a unique, undamped vibrating system, of a specified type, from specified vibratory behaviour, particularly specified natural frequencies and/or natural mode shapes. In this new edition the scope of the book has been widened to include topics such as isospectral systems- families of systems which all exhibit some specified behaviour; applications of the concept of Toda flow; new, non-classical approaches to inverse Sturm-Liouville problems; qualitative properties of the modes of some finite element models; damage identification. With its emphasis on analysis, on qualitative results, rather than on computation, the book will appeal to researchers in vibration theory, matrix analysis, differential and integral equations, matrix analysis, non-destructive testing, modal analysis, vibration isolation, etc. "This book is a necessary addition to the library of engineers and mathematicians working in vibration theory." Mathematical Reviews
Book Synopsis The Method of Approximate Inverse: Theory and Applications by : Thomas Schuster
Download or read book The Method of Approximate Inverse: Theory and Applications written by Thomas Schuster and published by Springer. This book was released on 2007-04-26 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with the method of approximate inverse which is a regularization technique for stably solving inverse problems in various settings. It demonstrates the performance and functionality of the method on several examples from medical imaging and non-destructive testing, such as computerized tomography, Doppler tomography, SONAR, X-ray diffractometry and thermoacoustic computerized tomography.
Book Synopsis Transport Phenomena and Kinetic Theory by : Carlo Cercignani
Download or read book Transport Phenomena and Kinetic Theory written by Carlo Cercignani and published by Springer Science & Business Media. This book was released on 2007-12-03 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of kinetic equations related to gases, semiconductors, photons, traffic flow, and other systems has developed rapidly in recent years because of its role as a mathematical tool in areas such as engineering, meteorology, biology, chemistry, materials science, nanotechnology, and pharmacy. Written by leading specialists in their respective fields, this book presents an overview of recent developments in the field of mathematical kinetic theory with a focus on modeling complex systems, emphasizing both mathematical properties and their physical meaning. Transport Phenomena and Kinetic Theory is an excellent self-study reference for graduate students, researchers, and practitioners working in pure and applied mathematics, mathematical physics, and engineering. The work may be used in courses or seminars on selected topics in transport phenomena or applications of the Boltzmann equation.
Book Synopsis Computational Methods in Physics by : Simon Širca
Download or read book Computational Methods in Physics written by Simon Širca and published by Springer. This book was released on 2018-06-21 with total page 880 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Methods for Solving Inverse Problems in Mathematical Physics by : Global Express Ltd. Co.
Download or read book Methods for Solving Inverse Problems in Mathematical Physics written by Global Express Ltd. Co. and published by CRC Press. This book was released on 2000-03-21 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developing an approach to the question of existence, uniqueness and stability of solutions, this work presents a systematic elaboration of the theory of inverse problems for all principal types of partial differential equations. It covers up-to-date methods of linear and nonlinear analysis, the theory of differential equations in Banach spaces, app
Book Synopsis The Factorization Method for Inverse Problems by : Andreas Kirsch
Download or read book The Factorization Method for Inverse Problems written by Andreas Kirsch and published by Oxford University Press. This book was released on 2008 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 'factorization method', discovered by Professor Kirsch, is a relatively new method for solving certain types of inverse scattering problems and problems in tomography. The text introduces the reader to this promising approach and discusses the wide applicability of this method by choosing typical examples.
Book Synopsis Inverse Problems and Related Topics by : Jin Cheng
Download or read book Inverse Problems and Related Topics written by Jin Cheng and published by Springer Nature. This book was released on 2020-02-04 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 13 chapters, which are extended versions of the presentations at International Conference on Inverse Problems at Fudan University, Shanghai, China, October 12-14, 2018, in honor of Masahiro Yamamoto on the occasion of his 60th anniversary. The chapters are authored by world-renowned researchers and rising young talents, and are updated accounts of various aspects of the researches on inverse problems. The volume covers theories of inverse problems for partial differential equations, regularization methods, and related topics from control theory. This book addresses a wide audience of researchers and young post-docs and graduate students who are interested in mathematical sciences as well as mathematics.
Book Synopsis Factorization, Singular Operators and Related Problems by : Stefan Samko
Download or read book Factorization, Singular Operators and Related Problems written by Stefan Samko and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings comprise a large part of the papers presented at the In ternational Conference Factorization, Singular Operators and related problems, which was held from January 28 to February 1, 2002, at the University of th Madeira, Funchal, Portugal, to mark Professor Georgii Litvinchuk's 70 birth day. Experts in a variety of fields came to this conference to pay tribute to the great achievements of Professor Georgii Litvinchuk in the development of vari ous areas of operator theory. The main themes of the conference were focussed around the theory of singular type operators and factorization problems, but other topics such as potential theory and fractional calculus, to name but a couple, were also presented. The goal of the conference was to bring together mathematicians from var ious fields within operator theory and function theory in order to highlight recent advances in problems many of which were originally studied by Profes sor Litvinchuk and his scientific school. A second aim was to stimulate in ternational collaboration even further and promote the interaction of different approaches in current research in these areas. The Proceedings will be of great interest to researchers in Operator The ory, Real and Complex Analysis, Functional and Harmonic Analysis, Potential Theory, Fractional Calculus and other areas, as well as to graduate students looking for the latest results.
Book Synopsis High Performance Computing and Applications by : Wu Zhang
Download or read book High Performance Computing and Applications written by Wu Zhang and published by Springer. This book was released on 2010-03-10 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Second International Conference on High-Performance Computing and Appli- tions (HPCA 2009) was a follow-up event of the successful HPCA 2004. It was held in Shanghai, a beautiful, active, and modern city in China, August 10–12, 2009. It served as a forum to present current work by researchers and software developers from around the world as well as to highlight activities in the high-performance c- puting area. It aimed to bring together research scientists, application pioneers, and software developers to discuss problems and solutions and to identify new issues in this area. This conference emphasized the development and study of novel approaches for high-performance computing, the design and analysis of high-performance - merical algorithms, and their scientific, engineering, and industrial applications. It offered the conference participants a great opportunity to exchange the latest research results, heighten international collaboration, and discuss future research ideas in HPCA. In addition to 24 invited presentations, the conference received over 300 contr- uted submissions from over ten countries and regions worldwide, about 70 of which were accepted for presentation at HPCA 2009. The conference proceedings contain some of the invited presentations and contributed submissions, and cover such research areas of interest as numerical algorithms and solutions, high-performance and grid c- puting, novel approaches to high-performance computing, massive data storage and processing, hardware acceleration, and their wide applications.
Book Synopsis Discrete Inverse Problems by : Per Christian Hansen
Download or read book Discrete Inverse Problems written by Per Christian Hansen and published by SIAM. This book was released on 2010-01-01 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, we demonstrate that insight about them goes hand in hand with algorithms.
