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Author : Grace Wahba
Publisher :
ISBN 13 :
Total Pages : 40 pages
Book Rating : 4.:/5 (253 download)
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:
Author : Grace Wahba
Publisher :
ISBN 13 :
Total Pages : 45 pages
Book Rating : 4.:/5 (227 download)
Download or read book Convergence Properties of the Method of Regularization for Noisy Linear Operation Equations written by Grace Wahba and published by . This book was released on 1973 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convergence properties of the method of regulation for finding approximate solutions to the linear operator equation g = Kf are found when g is contaminated by noise. If f belongs to (H sub R), a reproducing kernel Hilbert Space and K((H sub R)) = (H sub Q), another r.k.h.s. which is topologically equivalent to W2(m), it is shown how the optimum choice of lambda depends on n, m, the mean square noise, and f. (Author).
Author : Willi Freeden
Publisher : American Mathematical Society
ISBN 13 : 1470473453
Total Pages : 505 pages
Book Rating : 4.4/5 (74 download)
Download or read book Recovery Methodologies: Regularization and Sampling written by Willi Freeden and published by American Mathematical Society. This book was released on 2023-08-21 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to introduce the reader to methodologies in recovery problems for objects, such as functions and signals, from partial or indirect information. The recovery of objects from a set of data demands key solvers of inverse and sampling problems. Until recently, connections between the mathematical areas of inverse problems and sampling were rather tenuous. However, advances in several areas of mathematical research have revealed deep common threads between them, which proves that there is a serious need for a unifying description of the underlying mathematical ideas and concepts. Freeden and Nashed present an integrated approach to resolution methodologies from the perspective of both these areas. Researchers in sampling theory will benefit from learning about inverse problems and regularization methods, while specialists in inverse problems will gain a better understanding of the point of view of sampling concepts. This book requires some basic knowledge of functional analysis, Fourier theory, geometric number theory, constructive approximation, and special function theory. By avoiding extreme technicalities and elaborate proof techniques, it is an accessible resource for students and researchers not only from applied mathematics, but also from all branches of engineering and science.
Author : Heinz W. Engl
Publisher :
ISBN 13 :
Total Pages : 15 pages
Book Rating : 4.:/5 (255 download)
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:
Author : Thomas Schuster
Publisher : Walter de Gruyter
ISBN 13 : 3110255723
Total Pages : 296 pages
Book Rating : 4.1/5 (12 download)
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.
Author : Anatoly B. Bakushinsky
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110557355
Total Pages : 342 pages
Book Rating : 4.1/5 (15 download)
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 342 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
Author : Barbara Kaltenbacher
Publisher : Walter de Gruyter
ISBN 13 : 311020827X
Total Pages : 205 pages
Book Rating : 4.1/5 (12 download)
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.
Author : University of Wisconsin--Madison. Department of Statistics
Publisher :
ISBN 13 :
Total Pages : 732 pages
Book Rating : 4.:/5 (891 download)
Download or read book Technical Report written by University of Wisconsin--Madison. Department of Statistics and published by . This book was released on 1972 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Society for Industrial and Applied Mathematics
Publisher :
ISBN 13 :
Total Pages : 652 pages
Book Rating : 4.3/5 (121 download)
Download or read book SIAM Journal on Numerical Analysis written by Society for Industrial and Applied Mathematics and published by . This book was released on 1977 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains research articles on the development and analysis of numerical methods, including their convergence, stability, and error analysis as well as related results in functional analysis and approximation theory. Computational experiments and new types of numerical applications are also included.
Author : Torsten Hein
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832527451
Total Pages : 174 pages
Book Rating : 4.8/5 (325 download)
Download or read book Regularization in Banach Spaces - Convergence Rates Theory written by Torsten Hein and published by Logos Verlag Berlin GmbH. This book was released on 2010 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by their successful application in image restoring and sparsity reconstruction this manuscript deals with regularization theory of linear and nonlinear inverse and ill-posed problems in Banach space settings. Whereas regularization in Hilbert spaces has been widely studied in literature for a long period the developement and investigation of regularization methods in Banach spaces have become a field of modern research. The manuscript is twofolded. The first part deals with convergence rates theory for Tikhonov regularization as classical regularization method. In particular, generalizations of well-established results in Hilbert spaces are presented in the Banach space situation. Since the numerical effort of Tikhonov regularization in applications is rather high iterative approaches were considered as alternative regularization variants in the second part. In particular, two Gradient-type methods were presented and their behaviour concerning convergence and stability is investigated. For one of the methods, additionally, a convergence rates result is formulated. All the theoretical results are illustrated by some numerical examples.
Author :
Publisher : Springer-Verlag
ISBN 13 : 3322930343
Total Pages : 199 pages
Book Rating : 4.3/5 (229 download)
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:
Author : Bernd Hofmann
Publisher : Birkhäuser
ISBN 13 : 3319708244
Total Pages : 347 pages
Book Rating : 4.3/5 (197 download)
Download or read book New Trends in Parameter Identification for Mathematical Models written by Bernd Hofmann and published by Birkhäuser. This book was released on 2018-02-13 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings volume contains 16 contributions to the IMPA conference “New Trends in Parameter Identification for Mathematical Models”, Rio de Janeiro, Oct 30 – Nov 3, 2017, integrating the “Chemnitz Symposium on Inverse Problems on Tour”. This conference is part of the “Thematic Program on Parameter Identification in Mathematical Models” organized at IMPA in October and November 2017. One goal is to foster the scientific collaboration between mathematicians and engineers from the Brazialian, European and Asian communities. Main topics are iterative and variational regularization methods in Hilbert and Banach spaces for the stable approximate solution of ill-posed inverse problems, novel methods for parameter identification in partial differential equations, problems of tomography , solution of coupled conduction-radiation problems at high temperatures, and the statistical solution of inverse problems with applications in physics.
Author : Shuai Lu
Publisher : Walter de Gruyter
ISBN 13 : 3110286491
Total Pages : 304 pages
Book Rating : 4.1/5 (12 download)
Download or read book Regularization Theory for Ill-posed Problems written by Shuai Lu and published by Walter de Gruyter. This book was released on 2013-07-31 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a valuable contribution to the highly topical and extremly productive field of regularisation methods for inverse and ill-posed problems. The author is an internationally outstanding and accepted mathematician in this field. In his book he offers a well-balanced mixture of basic and innovative aspects. He demonstrates new, differentiated viewpoints, and important examples for applications. The book demontrates the current developments in the field of regularization theory, such as multiparameter regularization and regularization in learning theory. The book is written for graduate and PhD students and researchers in mathematics, natural sciences, engeneering, and medicine.
Author : United States. Army. Mathematics Research Center
Publisher :
ISBN 13 :
Total Pages : 242 pages
Book Rating : 4.3/5 (91 download)
Download or read book MRC Technical Summary Report written by United States. Army. Mathematics Research Center and published by . This book was released on 1976 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Andreas Kirsch
Publisher : Springer Nature
ISBN 13 : 3030633438
Total Pages : 412 pages
Book Rating : 4.0/5 (36 download)
Download or read book An Introduction to the Mathematical Theory of Inverse Problems written by Andreas Kirsch and published by Springer Nature. This book was released on 2021-02-15 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level textbook introduces the reader to the area of inverse problems, vital to many fields including geophysical exploration, system identification, nondestructive testing, and ultrasonic tomography. It aims to expose the basic notions and difficulties encountered with ill-posed problems, analyzing basic properties of regularization methods for ill-posed problems via several simple analytical and numerical examples. The book also presents three special nonlinear inverse problems in detail: the inverse spectral problem, the inverse problem of electrical impedance tomography (EIT), and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness, and continuous dependence on parameters. Ultimately, the text discusses theoretical results as well as numerical procedures for the inverse problems, including many exercises and illustrations to complement coursework in mathematics and engineering. This updated text includes a new chapter on the theory of nonlinear inverse problems in response to the field’s growing popularity, as well as a new section on the interior transmission eigenvalue problem which complements the Sturm-Liouville problem and which has received great attention since the previous edition was published.
Author : Dennis Trede
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832524665
Total Pages : 137 pages
Book Rating : 4.8/5 (325 download)
Download or read book Inverse Problems with Sparsity Constraints written by Dennis Trede and published by Logos Verlag Berlin GmbH. This book was released on 2010 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis contributes to the field of inverse problems with sparsity constraints. Since the pioneering work by Daubechies, Defries and De Mol in 2004, methods for solving operator equations with sparsity constraints play a central role in the field of inverse problems. This can be explained by the fact that the solutions of many inverse problems have a sparse structure, in other words, they can be represented using only finitely many elements of a suitable basis or dictionary. Generally, to stably solve an ill-posed inverse problem one needs additional assumptions on the unknown solution--the so-called source condition. In this thesis, the sparseness stands for the source condition, and with that in mind, stability results for two different approximation methods are deduced, namely, results for the Tikhonov regularization with a sparsity-enforcing penalty and for the orthogonal matching pursuit. The practical relevance of the theoretical results is shown with two examples of convolution type, namely, an example from mass spectrometry and an example from digital holography of particles.
Author : Heinz W. Engl
Publisher :
ISBN 13 :
Total Pages : 44 pages
Book Rating : 4.:/5 (255 download)
Download or read book Necessary and Sufficient Conditions for Convergence of Regularization Methods for Solving Linear Operator Equations of the First Kind written by Heinz W. Engl and published by . This book was released on 1980 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
