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Regularization Of Linear Operator Equations
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Book Synopsis Linear Operator Equations by : M. Thamban Nair
Download or read book Linear Operator Equations written by M. Thamban Nair and published by World Scientific. This book was released on 2009 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T 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 often be possible or may not be worth looking for due to physical constraints. In such situations, it is desirable to know how the so-called approximate solution approximates the exact solution, and what the error involved in such procedures would be. This book is concerned with the investigation of the above theoretical issues related to approximately solving linear operator equations. The main tools used for this purpose are basic results from functional analysis and some rudimentary ideas from numerical analysis. To make this book more accessible to readers, no in-depth knowledge on these disciplines is assumed for reading this book.
Book Synopsis Regularization of Linear Operator Equations by : Mark Anthony Lukas
Download or read book Regularization of Linear Operator Equations written by Mark Anthony Lukas and published by . This book was released on 1981 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Convergence Properties of the Method of Regularization for Noisy Linear Operator Equations by : Grace Wahba
Download or read book Convergence Properties of the Method of Regularization for Noisy Linear Operator Equations written by Grace Wahba and published by . This book was released on 1973 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Regularization Algorithms for Ill-Posed Problems by : Anatoly B. Bakushinsky
Download or read book Regularization Algorithms for Ill-Posed Problems written by Anatoly B. Bakushinsky and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-02-05 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Tikhonov-regularization of Ill-posed Linear Operator Equations on Closed Convex Sets by : Andreas Neubauer
Download or read book Tikhonov-regularization of Ill-posed Linear Operator Equations on Closed Convex Sets written by Andreas Neubauer and published by . This book was released on 1986 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Constrained Regularization for Ill Posed Linear Operator Equations, with Applications in Meteorology and Medicine by : Grace Wahba
Download or read book Constrained Regularization for Ill Posed Linear Operator Equations, with Applications in Meteorology and Medicine written by Grace Wahba and published by . This book was released on 1981 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: The relationship between certain regularization methods for solving ill posed linear operator equations and ridge methods in regression problems is described. The regularization estimates we describe may be viewed as ridge estimates in a (reproducing kernel) Hilbert space H. When the solution is known a priori to be in some closed, convex set in H, for example, the set of nonnegative functions, or the set of monotone functions, then one can propose regularized estimates subject to side conditions such as nonnegativity, monotonicity, etc. Some applications in medicine and meteorology are described. We describe the method of generalized cross validation for choosing the smoothing (or ridge) parameter in the presence of a family of linear inequality constraints. Some successful numerical examples, solving ill posed convolution equations with noisy data, subject to nonnegativity constraints, are presented. The technique appears to be quite successful in adding information, doing nearly the optimal amount of smoothing, and resolving distinct peaks in the solution which have been blurred by the convolution operation. (Author).
Book Synopsis On the Convergence of Regularization Methods for Ill-posed Linear Operator Equations by : Heinz W. Engl
Download or read book On the Convergence of Regularization Methods for Ill-posed Linear Operator Equations written by Heinz W. Engl and published by . This book was released on 1982 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Methods for Solving Operator Equations by : V. P. Tanana
Download or read book Methods for Solving Operator Equations written by V. P. Tanana and published by Walter de Gruyter. This book was released on 2012-02-13 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Generalized Inverses in Reproducing Kernel Spaces by : M. Zuhair Nashed
Download or read book Generalized Inverses in Reproducing Kernel Spaces written by M. Zuhair Nashed and published by . This book was released on 1972 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the paper a study of generalized inverses of linear operators in reproducing kernel Hilbert spaces (RKHS) is initiated. Explicit representations of generalized inverses in RKHS are obtained, and their relations to regularization of (ill-posed or poorly-conditioned) linear operator equations are explored. It is shown in particular that this approach provides a natural and effective setting for regularization problems when the operator maps one RKHS into another. Finally properties of the regularized pseudosolutions in this setting are studied. (Author).
Book Synopsis Approximate Regularized Solutions to Linear Operator Equations when the Data-vector is Not in the Range of the Operator by : M. Zuhair Nashed
Download or read book Approximate Regularized Solutions to Linear Operator Equations when the Data-vector is Not in the Range of the Operator written by M. Zuhair Nashed and published by . This book was released on 1973 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper addresses itself to the problem of approximate pseudo solutions of the linear operator equation Af = g, when g is not necessarily in the range of the operator A. (Modified author abstract).
Book Synopsis Regularization for Applied Inverse and Ill-Posed Problems by :
Download or read book Regularization for Applied Inverse and Ill-Posed Problems written by and published by Springer-Verlag. This book was released on 2013-11-22 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind by : C. W. Groetsch
Download or read book The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind written by C. W. Groetsch and published by Pitman Advanced Publishing Program. This book was released on 1984 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Regularization of Inverse Problems by : Heinz Werner Engl
Download or read book Regularization of Inverse Problems written by Heinz Werner Engl and published by Springer Science & Business Media. This book was released on 2000-03-31 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the mathematical theory of regularization methods and gives an account of the currently available results about regularization methods for linear and nonlinear ill-posed problems. Both continuous and iterative regularization methods are considered in detail with special emphasis on the development of parameter choice and stopping rules which lead to optimal convergence rates.
Book Synopsis Ill-Posed Problems with A Priori Information by : V. V. Vasin
Download or read book Ill-Posed Problems with A Priori Information written by V. V. Vasin and published by Walter de Gruyter. This book was released on 2013-02-18 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Local Regularization Methods for N-dimensional First-kind Integral Equations by : Changjun Cui
Download or read book Local Regularization Methods for N-dimensional First-kind Integral Equations written by Changjun Cui and published by . This book was released on 2005 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Mathematical Geodesy by : Willi Freeden
Download or read book Handbook of Mathematical Geodesy written by Willi Freeden and published by Birkhäuser. This book was released on 2018-06-11 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by leading experts, this book provides a clear and comprehensive survey of the “status quo” of the interrelating process and cross-fertilization of structures and methods in mathematical geodesy. Starting with a foundation of functional analysis, potential theory, constructive approximation, special function theory, and inverse problems, readers are subsequently introduced to today’s least squares approximation, spherical harmonics reflected spline and wavelet concepts, boundary value problems, Runge-Walsh framework, geodetic observables, geoidal modeling, ill-posed problems and regularizations, inverse gravimetry, and satellite gravity gradiometry. All chapters are self-contained and can be studied individually, making the book an ideal resource for both graduate students and active researchers who want to acquaint themselves with the mathematical aspects of modern geodesy.
