Computer Modelling In Tomography And Ill Posed Problems
DOWNLOAD
Download Computer Modelling In Tomography And Ill Posed Problems PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Computer Modelling In Tomography And Ill Posed Problems book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Computer Modelling In Tomography And Ill Posed Problems
DOWNLOAD
Author : Mikhail M. Lavrent'ev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-07-24
Computer Modelling In Tomography And Ill Posed Problems written by Mikhail M. Lavrent'ev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-24 with Mathematics categories.
Comparatively weakly researched untraditional tomography problems are solved because of new achievements in calculation mathematics and the theory of ill-posed problems, the regularization process of solving ill-posed problems, and the increase of stability. Experiments show possibilities and applicability of algorithms of processing tomography data. This monograph is devoted to considering these problems in connection with series of ill-posed problems in tomography settings arising from practice.The book includes chapters to the following themes: Mathematical basis of the method of computerized tomography Cone-beam tomography reconstruction Inverse kinematic problem in the tomographic setting
Computer Modelling In Tomography And Ill Posed Problems
DOWNLOAD
Author : Michail M. Lavrent'ev
language : en
Publisher: VSP
Release Date : 2001-01-01
Computer Modelling In Tomography And Ill Posed Problems written by Michail M. Lavrent'ev and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Computers categories.
The last decades of the 20th century were marked by the appearance of a new field of mathematics: computerized tomography. Its theory forms the basis for the solution of many applied problems. The methods of computerized tomography make it possible study the interior structure of a body by examining the characteristics of radiation passing through the object under study (transmission tomography). Depending on the type of radiation used, X-ray, optical, seismic, and some other kinds of tomography can be distinguished. Comparatively weakly researched, untraditional tomography problems are being solved because of new achievements in calculation mathematics and the theory of ill-posed problems (3D cone-beam tomography, geo-tomography). Experiments show possibilities and applicability of algorithms of processing tomography data. This monograph is devoted to considering these problems in connection with series of ill-posed problems in tomography settings, arising from practice. The basic themes of the book are: mathematical basis of the method of computerized tomography; algorithms for 3D cone-beam tomography; and inverse kinematics problems in tomographic settings (geo-tomography). This volume in the Inverse and Ill-Posed Problems Series will be of interest to researchers, graduates and post-graduates in X-ray, optical, seismic, as well as some other kinds of tomography in both academia and industry.
Operator Theory And Ill Posed Problems
DOWNLOAD
Author : Mikhail M. Lavrent'ev
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-22
Operator Theory And Ill Posed Problems written by Mikhail M. Lavrent'ev and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-22 with Mathematics categories.
This book consists of three major parts. The first two parts deal with general mathematical concepts and certain areas of operator theory. The third part is devoted to ill-posed problems. It can be read independently of the first two parts and presents a good example of applying the methods of calculus and functional analysis. The first part "Basic Concepts" briefly introduces the language of set theory and concepts of abstract, linear and multilinear algebra. Also introduced are the language of topology and fundamental concepts of calculus: the limit, the differential, and the integral. A special section is devoted to analysis on manifolds. The second part "Operators" describes the most important function spaces and operator classes for both linear and nonlinear operators. Different kinds of generalized functions and their transformations are considered. Elements of the theory of linear operators are presented. Spectral theory is given a special focus. The third part "Ill-Posed Problems" is devoted to problems of mathematical physics, integral and operator equations, evolution equations and problems of integral geometry. It also deals with problems of analytic continuation. Detailed coverage of the subjects and numerous examples and exercises make it possible to use the book as a textbook on some areas of calculus and functional analysis. It can also be used as a reference textbook because of the extensive scope and detailed references with comments.
Ill Posed And Non Classical Problems Of Mathematical Physics And Analysis
DOWNLOAD
Author : Mikhail M. Lavrent'ev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-07-24
Ill Posed And Non Classical Problems Of Mathematical Physics And Analysis written by Mikhail M. Lavrent'ev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-24 with Mathematics categories.
These proceedings of the international Conference "Ill-Posed and Non-Classical Problems of Mathematical Physics and Analysis", held at the Samarkand State University, Uzbekistan in September 2000 bring together fundamental research articles in the major areas of the numerated fields of analysis and mathematical physics. The book covers the following topics: theory of ill-posed problems inverse problems for differential equations boundary value problems for equations of mixed type integral geometry mathematical modelling and numerical methods in natural sciences
Well Posed Ill Posed And Intermediate Problems With Applications
DOWNLOAD
Author : Petrov Yuri P.
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-22
Well Posed Ill Posed And Intermediate Problems With Applications written by Petrov Yuri P. and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-22 with Mathematics categories.
This book deals with one of the key problems in applied mathematics, namely the investigation into and providing for solution stability in solving equations with due allowance for inaccuracies in set initial data, parameters and coefficients of a mathematical model for an object under study, instrumental function, initial conditions, etc., and also with allowance for miscalculations, including roundoff errors. Until recently, all problems in mathematics, physics and engineering were divided into two classes: well-posed problems and ill-posed problems. The authors introduce a third class of problems: intermediate ones, which are problems that change their property of being well- or ill-posed on equivalent transformations of governing equations, and also problems that display the property of being either well- or ill-posed depending on the type of the functional space used. The book is divided into two parts: Part one deals with general properties of all three classes of mathematical, physical and engineering problems with approaches to solve them; Part two deals with several stable models for solving inverse ill-posed problems, illustrated with numerical examples.
Ill Posed Boundary Value Problems
DOWNLOAD
Author : Serikkali E. Temirbolat
language : en
Publisher: Walter de Gruyter
Release Date : 2012-06-04
Ill Posed Boundary Value Problems written by Serikkali E. Temirbolat and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-04 with Mathematics categories.
This monograph extends well-known facts to new classes of problems and works out novel approaches to the solution of these problems. It is devoted to the questions of ill-posed boundary-value problems for systems of various types of the first-order differential equations with constant coefficients and the methods for their solution.
Computational Methods For Inverse Problems
DOWNLOAD
Author : Curtis R. Vogel
language : en
Publisher: SIAM
Release Date : 2002-01-01
Computational Methods For Inverse Problems written by Curtis R. Vogel and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.
Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
Poorly Visible Media In X Ray Tomography
DOWNLOAD
Author : V. G. Nazarov
language : en
Publisher: VSP
Release Date : 2002-01-01
Poorly Visible Media In X Ray Tomography written by V. G. Nazarov and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Science categories.
The tomography problem considered in this volume of the Inverse and Ill-Posed Problems Series consists of finding an essential part of information about the internal structure of an unknown medium. More particularly, the contact boundaries between various materials in the medium are sought. This investigation is implemented by studying an appropriate mathematical model, which is represented as a transport equation (linear Boltzmann's equation) together with certain boundary conditions. Both theoretical and numerical methods have been used and the results consist of proved theorems, computer testing of the corresponding algorithms, together with a number of tables. This book may be considered as a continuation and application of Transport Equation and Tomography by D.S. Anikonov, A.E. Kovtanyuk and I.V. Prokhorov, previously published in this series.
Inverse And Ill Posed Problems
DOWNLOAD
Author : Sergey I. Kabanikhin
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-23
Inverse And Ill Posed Problems written by Sergey I. Kabanikhin and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-23 with Mathematics categories.
The theory of ill-posed problems originated in an unusual way. As a rule, a new concept is a subject in which its creator takes a keen interest. The concept of ill-posed problems was introduced by Hadamard with the comment that these problems are physically meaningless and not worthy of the attention of serious researchers. Despite Hadamard's pessimistic forecasts, however, his unloved "child" has turned into a powerful theory whose results are used in many fields of pure and applied mathematics. What is the secret of its success? The answer is clear. Ill-posed problems occur everywhere and it is unreasonable to ignore them. Unlike ill-posed problems, inverse problems have no strict mathematical definition. In general, they can be described as the task of recovering a part of the data of a corresponding direct (well-posed) problem from information about its solution. Inverse problems were first encountered in practice and are mostly ill-posed. The urgent need for their solution, especially in geological exploration and medical diagnostics, has given powerful impetus to the development of the theory of ill-posed problems. Nowadays, the terms "inverse problem" and "ill-posed problem" are inextricably linked to each other. Inverse and ill-posed problems are currently attracting great interest. A vast literature is devoted to these problems, making it necessary to systematize the accumulated material. This book is the first small step in that direction. We propose a classification of inverse problems according to the type of equation, unknowns and additional information. We consider specific problems from a single position and indicate relationships between them. The problems relate to different areas of mathematics, such as linear algebra, theory of integral equations, integral geometry, spectral theory and mathematical physics. We give examples of applied problems that can be studied using the techniques we describe. This book was conceived as a textbook on the foundations of the theory of inverse and ill-posed problems for university students. The author's intention was to explain this complex material in the most accessible way possible. The monograph is aimed primarily at those who are just beginning to get to grips with inverse and ill-posed problems but we hope that it will be useful to anyone who is interested in the subject.
Medical Image Computing And Computer Assisted Intervention Miccai 2001
DOWNLOAD
Author : Wiro J. Niessen
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-10-02
Medical Image Computing And Computer Assisted Intervention Miccai 2001 written by Wiro J. Niessen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-10-02 with Computers categories.
This book constitutes the refereed proceedings of the 4th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2001, held in Utrecht, The Netherlands, in October 2001. The 122 revised papers and 136 posters presented were carefully reviewed and selected from a total of 338 submissions. The book offers topical sections on image-guided surgery; shape analysis, segmentation, computer-aided diagnosis; registration; simulation, planning and modeling; visualization; quantitative image analysis; medical robotics and devices; visualization and augmented reality; and time series analysis.