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Author: V. V. Vasin
Publisher: Walter de Gruyter
ISBN: 3110900114
Category : Mathematics
Languages : en
Pages : 268
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Book Description
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.
Author: V. V. Vasin
Publisher: Walter de Gruyter
ISBN: 3110900114
Category : Mathematics
Languages : en
Pages : 268
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Book Description
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.
Author: A.N. Tikhonov
Publisher: Springer Science & Business Media
ISBN: 940158480X
Category : Mathematics
Languages : en
Pages : 257
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Book Description
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.
Author: Anatoly B. Bakushinsky
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110556383
Category : Mathematics
Languages : en
Pages : 447
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Book Description
This specialized and authoritative book contains an overview of modern approaches to constructing approximations to solutions of ill-posed operator equations, both linear and nonlinear. These approximation schemes form a basis for implementable numerical algorithms for the stable solution of operator equations arising in contemporary mathematical modeling, and in particular when solving inverse problems of mathematical physics. The book presents in detail stable solution methods for ill-posed problems using the methodology of iterative regularization of classical iterative schemes and the techniques of finite dimensional and finite difference approximations of the problems under study. Special attention is paid to ill-posed Cauchy problems for linear operator differential equations and to ill-posed variational inequalities and optimization problems. The readers are expected to have basic knowledge in functional analysis and differential equations. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems, and also to advanced students in these fields. Contents Introduction Regularization Methods For Linear Equations Finite Difference Methods Iterative Regularization Methods Finite-Dimensional Iterative Processes Variational Inequalities and Optimization Problems
Author: Bernd Hofmann
Publisher: Springer
ISBN:
Category : Technology & Engineering
Languages : en
Pages : 204
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Book Description
Author: G.S. Dulikravich
Publisher: Elsevier
ISBN: 0080535143
Category : Computers
Languages : en
Pages : 433
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Book Description
Inverse Problems are found in many areas of engineering mechanics and there are many successful applications e.g. in non-destructive testing and characterization of material properties by ultrasonic or X-ray techniques, thermography, etc. Generally speaking, inverse problems are concerned with the determination of the input and the characteristics of a system, given certain aspects of its output. Mathematically, such problems are ill-posed and have to be overcome through development of new computational schemes, regularization techniques, objective functionals, and experimental procedures. This volume contains a selection of peer-reviewed papers presented at the International Symposium on Inverse Problems in Engineering Mechanics (ISIP2001), held in February of 2001 in Nagano, Japan, where recent development in inverse problems in engineering mechanics and related topics were discussed. The following general areas in inverse problems in engineering mechanics were the subjects of the ISIP2001: mathematical and computational aspects of inverse problems, parameter or system identification, shape determination, sensitivity analysis, optimization, material property characterization, ultrasonic non-destructive testing, elastodynamic inverse problems, thermal inverse problems, and other engineering applications. These papers can provide a state-of-the-art review of the research on inverse problems in engineering mechanics.
Author: Yanfei Wang
Publisher: Springer Science & Business Media
ISBN: 3642137423
Category : Mathematics
Languages : en
Pages : 354
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Book Description
"Optimization and Regularization for Computational Inverse Problems and Applications" focuses on advances in inversion theory and recent developments with practical applications, particularly emphasizing the combination of optimization and regularization for solving inverse problems. This book covers both the methods, including standard regularization theory, Fejer processes for linear and nonlinear problems, the balancing principle, extrapolated regularization, nonstandard regularization, nonlinear gradient method, the nonmonotone gradient method, subspace method and Lie group method; and the practical applications, such as the reconstruction problem for inverse scattering, molecular spectra data processing, quantitative remote sensing inversion, seismic inversion using the Lie group method, and the gravitational lensing problem. Scientists, researchers and engineers, as well as graduate students engaged in applied mathematics, engineering, geophysics, medical science, image processing, remote sensing and atmospheric science will benefit from this book. Dr. Yanfei Wang is a Professor at the Institute of Geology and Geophysics, Chinese Academy of Sciences, China. Dr. Sc. Anatoly G. Yagola is a Professor and Assistant Dean of the Physical Faculty, Lomonosov Moscow State University, Russia. Dr. Changchun Yang is a Professor and Vice Director of the Institute of Geology and Geophysics, Chinese Academy of Sciences, China.
Author: F.P. Vasilyev
Publisher: Springer Science & Business Media
ISBN: 9401597596
Category : Mathematics
Languages : en
Pages : 320
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Book Description
Along with the traditional material concerning linear programming (the simplex method, the theory of duality, the dual simplex method), In-Depth Analysis of Linear Programming contains new results of research carried out by the authors. For the first time, the criteria of stability (in the geometrical and algebraic forms) of the general linear programming problem are formulated and proved. New regularization methods based on the idea of extension of an admissible set are proposed for solving unstable (ill-posed) linear programming problems. In contrast to the well-known regularization methods, in the methods proposed in this book the initial unstable problem is replaced by a new stable auxiliary problem. This is also a linear programming problem, which can be solved by standard finite methods. In addition, the authors indicate the conditions imposed on the parameters of the auxiliary problem which guarantee its stability, and this circumstance advantageously distinguishes the regularization methods proposed in this book from the existing methods. In these existing methods, the stability of the auxiliary problem is usually only presupposed but is not explicitly investigated. In this book, the traditional material contained in the first three chapters is expounded in much simpler terms than in the majority of books on linear programming, which makes it accessible to beginners as well as those more familiar with the area.
Author: Konstantin P. Gaikovich
Publisher: Nova Publishers
ISBN: 9781594540950
Category : Mathematics
Languages : en
Pages : 392
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Book Description
Unlike direct problems related to the solution of differential equations, inverse problems are typically expressed by integral equations. These equations relate media parameters to parameters of a measured signal, or input parameters to output ones in various measurement systems. The solution of integral equations is, with few exceptions, an ill-posed problem, and additional a priori information about the exact solution should be used to solve such problems. The specific character of the a priori information determines various regularisation methods that are in use here to obtain an approximate solution: Tikhonov's method, statistical regularisation method, methods based on the use of additional equations or restrictions or of models with limited number of unknown parameters. The main point of this book is the study of convergence properties of each method and the wide application of numerical modelling that gives the accuracy of the solution in a chosen metric. It is an unaccustomed procedure for physicists, but, because there is no proportionality between data and solution errors in ill-posed problems, such approach is inevitable.
Author: Vladimir M. Krasnopolsky
Publisher: Springer Science & Business Media
ISBN: 9400760736
Category : Science
Languages : en
Pages : 205
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Book Description
This book brings together a representative set of Earth System Science (ESS) applications of the neural network (NN) technique. It examines a progression of atmospheric and oceanic problems, which, from the mathematical point of view, can be formulated as complex, multidimensional, and nonlinear mappings. It is shown that these problems can be solved utilizing a particular type of NN – the multilayer perceptron (MLP). This type of NN applications covers the majority of NN applications developed in ESSs such as meteorology, oceanography, atmospheric and oceanic satellite remote sensing, numerical weather prediction, and climate studies. The major properties of the mappings and MLP NNs are formulated and discussed. Also, the book presents basic background for each introduced application and provides an extensive set of references. “This is an excellent book to learn how to apply artificial neural network methods to earth system sciences. The author, Dr. Vladimir Krasnopolsky, is a universally recognized master in this field. With his vast knowledge and experience, he carefully guides the reader through a broad variety of problems found in the earth system sciences where neural network methods can be applied fruitfully. (...) The broad range of topics covered in this book ensures that researchers/graduate students from many fields (...) will find it an invaluable guide to neural network methods.” (Prof. William W. Hsieh, University of British Columbia, Vancouver, Canada) “Vladimir Krasnopolsky has been the “founding father” of applying computation intelligence methods to environmental science; (...) Dr. Krasnopolsky has created a masterful exposition of a young, yet maturing field that promises to advance a deeper understanding of best modeling practices in environmental science.” (Dr. Sue Ellen Haupt, National Center for Atmospheric Research, Boulder, USA) “Vladimir Krasnopolsky has written an important and wonderful book on applications of neural networks to replace complex and expensive computational algorithms within Earth System Science models. He is uniquely qualified to write this book, since he has been a true pioneer with regard to many of these applications. (...) Many other examples of creative emulations will inspire not just readers interested in the Earth Sciences, but any other modeling practitioner (...) to address both theoretical and practical complex problems that may (or will!) arise in a complex system." ” (Prof. Eugenia Kalnay, University of Maryland, USA)
Author: Mukesh Khare
Publisher: BoD – Books on Demand
ISBN: 9535104241
Category : Technology & Engineering
Languages : en
Pages : 399
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Book Description
Air pollution has always been a trans-boundary environmental problem and a matter of global concern for past many years. High concentrations of air pollutants due to numerous anthropogenic activities influence the air quality. There are many books on this subject, but the one in front of you will probably help in filling the gaps existing in the area of air quality monitoring, modelling, exposure, health and control, and can be of great help to graduate students professionals and researchers. The book is divided in two volumes dealing with various monitoring techniques of air pollutants, their predictions and control. It also contains case studies describing the exposure and health implications of air pollutants on living biota in different countries across the globe.
