Download or read book Iterative Methods for Ill posed Boundary Value Problems written by George Bastay and published by . This book was released on 1995 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Iterative Methods for Ill Posed Problems written by Anatoly B. Bakushinsky and published by Walter de Gruyter. This book was released on 2010-12-23 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ill-posed problems are encountered in countless areas of real world science and technology. A variety of processes in science and engineering is commonly modeled by algebraic, differential, integral and other equations. In a more difficult case, it can be systems of equations combined with the associated initial and boundary conditions. Frequently, the study of applied optimization problems is also reduced to solving the corresponding equations. These equations, encountered both in theoretical and applied areas, may naturally be classified as operator equations. The current textbook will focus on iterative methods for operator equations in Hilbert spaces.

Download or read book Iterative Methods for Ill posed Problems written by Anatoly B. Bakushinsky and published by Walter de Gruyter. This book was released on 2011 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ill-posed problems are encountered in countless areas of real world science and technology. A variety of processes in science and engineering is commonly modeled by algebraic, differential, integral and other equations. In a more difficult case, it can be systems of equations combined with the associated initial and boundary conditions. Frequently, the study of applied optimization problems is also reduced to solving the corresponding equations. These equations, encountered both in theoretical and applied areas, may naturally be classified as operator equations. The current textbook will focus on iterative methods for operator equations in Hilbert spaces.

Download or read book Iterative Methods for Solving Inverse and Ill posed Problems with Data Given on the Part of the Boundary written by Sergey I. Kabanikhin and published by Walter de Gruyter. This book was released on 2013-04-20 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solving inverse problems means the determination of shape or consistency of inaccessible objects from indirect measurements. Those problems arise in many applications, e.g., medical imaging and earth surface explorations. The mathematical modelling of some of those problems leads to inverse problems for boundary value problems for differential equations with incomplete given data. The present book provides an introduction to the numerical solution of the latter class of problems.

Download or read book Refined Iterative Methods for Computation of the Solution and the Eigenvalues of Self Adjoint Boundary Value Problems written by ENGELI and published by Birkhäuser. This book was released on 2012-12-06 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Inverse and Ill Posed Problems written by Heinz W. Engl and published by Elsevier. This book was released on 2014-05-10 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse and Ill-Posed Problems is a collection of papers presented at a seminar of the same title held in Austria in June 1986. The papers discuss inverse problems in various disciplines; mathematical solutions of integral equations of the first kind; general considerations for ill-posed problems; and the various regularization methods for integral and operator equations of the first kind. Other papers deal with applications in tomography, inverse scattering, detection of radiation sources, optics, partial differential equations, and parameter estimation problems. One paper discusses three topics on ill-posed problems, namely, the imposition of specified types of discontinuities on solutions of ill-posed problems, the use of generalized cross validation as a data based termination rule for iterative methods, and also a parameter estimation problem in reservoir modeling. Another paper investigates a statistical method to determine the truncation level in Eigen function expansions and for Fredholm equations of the first kind where the data contains some errors. Another paper examines the use of singular function expansions in the inversion of severely ill-posed problems arising in confocal scanning microscopy, particle sizing, and velocimetry. The collection can benefit many mathematicians, students, and professor of calculus, statistics, and advanced mathematics.

Download or read book Regularization of Ill Posed Problems by Iteration Methods written by S.F. Gilyazov and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iteration regularization, i.e., utilization of iteration methods of any form for the stable approximate solution of ill-posed problems, is one of the most important but still insufficiently developed topics of the new theory of ill-posed problems. In this monograph, a general approach to the justification of iteration regulari zation algorithms is developed, which allows us to consider linear and nonlinear methods from unified positions. Regularization algorithms are the 'classical' iterative methods (steepest descent methods, conjugate direction methods, gradient projection methods, etc.) complemented by the stopping rule depending on level of errors in input data. They are investigated for solving linear and nonlinear operator equations in Hilbert spaces. Great attention is given to the choice of iteration index as the regularization parameter and to estimates of errors of approximate solutions. Stabilizing properties such as smoothness and shape constraints imposed on the solution are used. On the basis of these investigations, we propose and establish efficient regularization algorithms for stable numerical solution of a wide class of ill-posed problems. In particular, descriptive regularization algorithms, utilizing a priori information about the qualitative behavior of the sought solution and ensuring a substantial saving in computational costs, are considered for model and applied problems in nonlinear thermophysics. The results of calculations for important applications in various technical fields (a continuous casting, the treatment of materials and perfection of heat-protective systems using laser and composite technologies) are given.

Download or read book Analysis of the Robin Dirichlet iterative procedure for solving the Cauchy problem for elliptic equations with extension to unbounded domains written by Pauline Achieng and published by Linköping University Electronic Press. This book was released on 2020-10-26 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we study the Cauchy problem for elliptic equations. It arises in many areas of application in science and engineering as a problem of reconstruction of solutions to elliptic equations in a domain from boundary measurements taken on a part of the boundary of this domain. The Cauchy problem for elliptic equations is known to be ill-posed. We use an iterative regularization method based on alternatively solving a sequence of well-posed mixed boundary value problems for the same elliptic equation. This method, based on iterations between Dirichlet-Neumann and Neumann-Dirichlet mixed boundary value problems was first proposed by Kozlov and Maz’ya [13] for Laplace equation and Lame’ system but not Helmholtz-type equations. As a result different modifications of this original regularization method have been proposed in literature. We consider the Robin-Dirichlet iterative method proposed by Mpinganzima et.al [3] for the Cauchy problem for the Helmholtz equation in bounded domains. We demonstrate that the Robin-Dirichlet iterative procedure is convergent for second order elliptic equations with variable coefficients provided the parameter in the Robin condition is appropriately chosen. We further investigate the convergence of the Robin-Dirichlet iterative procedure for the Cauchy problem for the Helmholtz equation in a an unbounded domain. We derive and analyse the necessary conditions needed for the convergence of the procedure. In the numerical experiments, the precise behaviour of the procedure for different values of k2 in the Helmholtz equation is investigated and the results show that the speed of convergence depends on the choice of the Robin parameters, ?0 and ?1. In the unbounded domain case, the numerical experiments demonstrate that the procedure is convergent provided that the domain is truncated appropriately and the Robin parameters, ?0 and ?1 are also chosen appropriately.

Download or read book Handbook of Mathematical Methods in Imaging written by Otmar Scherzer and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

Download or read book Iterative Methods and Their Dynamics with Applications written by Ioannis Konstantinos Argyros and published by CRC Press. This book was released on 2017-07-12 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iterative processes are the tools used to generate sequences approximating solutions of equations describing real life problems. Intended for researchers in computational sciences and as a reference book for advanced computational method in nonlinear analysis, this book is a collection of the recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces and presents several applications and connections with fixed point theory. It contains an abundant and updated bibliography and provides comparisons between various investigations made in recent years in the field of computational nonlinear analysis. The book also provides recent advancements in the study of iterative procedures and can be used as a source to obtain the proper method to use in order to solve a problem. The book assumes a basic background in Mathematical Statistics, Linear Algebra and Numerical Analysis and may be used as a self-study reference or as a supplementary text for an advanced course in Biosciences or Applied Sciences. Moreover, the newest techniques used to study the dynamics of iterative methods are described and used in the book and they are compared with the classical ones.

Download or read book Refined Iterative Methods for Computation of the Solution and the Eigenvalues of Self Adjoint Boundary Value Problems written by M. Engeli and published by Birkhauser. This book was released on 1980-01-01 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Methods for Solving Inverse Problems of Mathematical Physics written by A. A. Samarskii and published by Walter de Gruyter. This book was released on 2008-08-27 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main classes of inverse problems for equations of mathematical physics and their numerical solution methods are considered in this book which is intended for graduate students and experts in applied mathematics, computational mathematics, and mathematical modelling.

Download or read book Iterative Regularization Methods for Nonlinear Ill Posed Problems written by Barbara Kaltenbacher and published by Walter de Gruyter. This book was released on 2008-09-25 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear inverse problems appear in many applications, and typically they lead to mathematical models that are ill-posed, i.e., they are unstable under data perturbations. Those problems require a regularization, i.e., a special numerical treatment. This book presents regularization schemes which are based on iteration methods, e.g., nonlinear Landweber iteration, level set methods, multilevel methods and Newton type methods.

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.

Download or read book Computational Optimal Control written by Roland Bulirsch and published by Birkhäuser. This book was released on 2012-12-06 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Resources should be used sparingly both from a point of view of economy and eco logy. Thus in controlling industrial, economical and social processes, optimization is the tool of choice. In this area of applied numerical analysis, the INTERNATIONAL FEDERATION OF AUTOMATIC CONTROL (IFAC) acts as a link between research groups in universities, national research laboratories and industry. For this pur pose, the technical committee Mathematics of Control of IFAC organizes biennial conferences with the objective of bringing together experts to exchange ideas, ex periences and future developments in control applications of optimization. There should be a genuine feedback loop between mathematicians, computer scientists, engineers and software developers. This loop should include the design, application and implementation of algorithms. The contributions of industrial practitioners are especially important. These proceedings contain selected papers from a workshop on CONTROL Ap PLICATIONS OF OPTIMIZATION, which took place at the Fachhochschule Miinchen in September 1992. The workshop was the ninth in a series of very successful bien nial meetings, starting with the Joint Automatic Control Conference in Denver in 1978 and followed by conferences in London, Oberpfaffenhofen, San Francisco, Ca pri, Tbilisi and Paris. The workshop was attended by ninety researchers from four continents. This volume represents the state of the art in the field, with emphasis on progress made since the publication of the proceedings of the Capri meeting, edited by G. di Pillo under the title 'Control Applications of Optimization and Nonlinear Programming'.

Download or read book Numerical Methods for Inverse Problems written by Michel Kern and published by John Wiley & Sons. This book was released on 2016-03-31 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies methods to concretely address inverse problems. An inverse problem arises when the causes that produced a given effect must be determined or when one seeks to indirectly estimate the parameters of a physical system. The author uses practical examples to illustrate inverse problems in physical sciences. He presents the techniques and specific methods chosen to solve inverse problems in a general domain of application, choosing to focus on a small number of methods that can be used in most applications. This book is aimed at readers with a mathematical and scientific computing background. Despite this, it is a book with a practical perspective. The methods described are applicable, have been applied, and are often illustrated by numerical examples.

Download or read book Ill Posed and Non Classical Problems of Mathematical Physics and Analysis written by Mikhail M. Lavrent'ev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-07-24 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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