[PDF] Nonlinear Ill Posed Problems Of Monotone Type eBook

Author : Yakov Alber
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 31,32 MB
Release : 2006-02-02
Category : Mathematics
ISBN : 9781402043956

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Interest in regularization methods for ill-posed nonlinear operator equations and variational inequalities of monotone type in Hilbert and Banach spaces has grown rapidly over recent years. Results in the field over the last three decades, previously only available in journal articles, are comprehensively explored with particular attention given to applications of regularization methods as well as to practical methods used in computational analysis.

Author : Yakov Alber
Publisher : Springer Science & Business Media
Page : 422 pages
File Size : 48,16 MB
Release : 2006-02-23
Category : Mathematics
ISBN : 1402043961

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Interest in regularization methods for ill-posed nonlinear operator equations and variational inequalities of monotone type in Hilbert and Banach spaces has grown rapidly over recent years. Results in the field over the last three decades, previously only available in journal articles, are comprehensively explored with particular attention given to applications of regularization methods as well as to practical methods used in computational analysis.

Author : Barbara Kaltenbacher
Publisher : Walter de Gruyter
Page : 205 pages
File Size : 15,43 MB
Release : 2008-09-25
Category : Mathematics
ISBN : 311020827X

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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.

Author : Athanass Kartsatos
Publisher : CRC Press
Page : 338 pages
File Size : 13,16 MB
Release : 1996-03-14
Category : Mathematics
ISBN : 9780824797218

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This work is based upon a Special Session on the Theory and Applications of Nonlinear Operators of Accretive and Monotone Type held during the recent meeting of the American Mathematical Society in San Francisco. It examines current developments in non-linear analysis, emphasizing accretive and monotone operator theory. The book presents a major survey/research article on partial functional differential equations with delay and an important survey/research article on approximation solvability.

Author : Anatoly B. Bakushinsky
Publisher : Walter de Gruyter GmbH & Co KG
Page : 342 pages
File Size : 47,42 MB
Release : 2018-02-05
Category : Mathematics
ISBN : 3110557355

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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 : Anatoly B. Bakushinsky
Publisher : Walter de Gruyter
Page : 153 pages
File Size : 21,87 MB
Release : 2011
Category : Mathematics
ISBN : 3110250640

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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.

Author : Alexander G. Ramm
Publisher : Springer Science & Business Media
Page : 453 pages
File Size : 36,8 MB
Release : 2005-12-19
Category : Technology & Engineering
ISBN : 0387232184

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Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.

Author : Dimitrios C. Kravvaritis
Publisher : Walter de Gruyter GmbH & Co KG
Page : 499 pages
File Size : 30,85 MB
Release : 2020-04-06
Category : Mathematics
ISBN : 3110647389

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This well-thought-out book covers the fundamentals of nonlinear analysis, with a particular focus on variational methods and their applications. Starting from preliminaries in functional analysis, it expands in several directions such as Banach spaces, fixed point theory, nonsmooth analysis, minimax theory, variational calculus and inequalities, critical point theory, monotone, maximal monotone and pseudomonotone operators, and evolution problems.

Author : Atef Ibrahim Elmahdy
Publisher : LAP Lambert Academic Publishing
Page : 100 pages
File Size : 19,22 MB
Release : 2012-04
Category :
ISBN : 9783848482627

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Many problems in science and engineering have their mathematical formulation as an operator equation of the form F(x) = y, where F is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not be often possible or may not be worth looking for due to physical constraints. In such situation, it is desirable to know how the so-called approximate solution approximates the exact solution, and what would be the error involved in such procedures. The main focus of the book is on the study of stably solving nonlinear ill posed operator equations of the form F(x)=y, with monotone nonlinear operator F in an infinite dimensional real Hilbert space X, that is , F obeys the monotonicity property. It is assumed that the exact data y is unknown and usually only noisy data are available. Problems of this type arise in a number of applications. Since the solution does not depend continuously on the data, the ill-posed problem has to be regularized. We considered iterative methods which converge to the unique solution of the method of Lavrentiev regularization.