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Approximate Regularized Solutions To Linear Operator Equations When The Data Vector Is Not In The Range Of The Operator
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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 Constructive and Computational Methods for Differential and Integral Equations by : D.L. Colton
Download or read book Constructive and Computational Methods for Differential and Integral Equations written by D.L. Colton and published by Springer. This book was released on 2006-11-15 with total page 488 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 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.
Book Synopsis Methods for Solving Operator Equations by : Vitalij P. Tanana
Download or read book Methods for Solving Operator Equations written by Vitalij P. Tanana and published by VSP. This book was released on 1997 with total page 236 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 MRC Technical Summary Report by : Mathematics Research Center (United States. Army)
Download or read book MRC Technical Summary Report written by Mathematics Research Center (United States. Army) and published by . This book was released on 1973 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Bulletin of the American Mathematical Society by :
Download or read book Bulletin of the American Mathematical Society written by and published by . This book was released on 1974 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Practical Approximate Solutions to Linear Operator Equations when the Data are Noisy by : Grace Wahba
Download or read book Practical Approximate Solutions to Linear Operator Equations when the Data are Noisy written by Grace Wahba and published by . This book was released on 1975 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Regularization for Atmospheric Inverse Problems by : Adrian Doicu
Download or read book Numerical Regularization for Atmospheric Inverse Problems written by Adrian Doicu and published by Springer Science & Business Media. This book was released on 2010-07-16 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The retrieval problems arising in atmospheric remote sensing belong to the class of the - called discrete ill-posed problems. These problems are unstable under data perturbations, and can be solved by numerical regularization methods, in which the solution is stabilized by taking additional information into account. The goal of this research monograph is to present and analyze numerical algorithms for atmospheric retrieval. The book is aimed at physicists and engineers with some ba- ground in numerical linear algebra and matrix computations. Although there are many practical details in this book, for a robust and ef?cient implementation of all numerical algorithms, the reader should consult the literature cited. The data model adopted in our analysis is semi-stochastic. From a practical point of view, there are no signi?cant differences between a semi-stochastic and a determin- tic framework; the differences are relevant from a theoretical point of view, e.g., in the convergence and convergence rates analysis. After an introductory chapter providing the state of the art in passive atmospheric remote sensing, Chapter 2 introduces the concept of ill-posedness for linear discrete eq- tions. To illustrate the dif?culties associated with the solution of discrete ill-posed pr- lems, we consider the temperature retrieval by nadir sounding and analyze the solvability of the discrete equation by using the singular value decomposition of the forward model matrix.
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 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
Download or read book Government Reports Index written by and published by . This book was released on 1973 with total page 1192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Proceedings of the National Conference by : Association for Computing Machinery
Download or read book Proceedings of the National Conference written by Association for Computing Machinery and published by . This book was released on 1973 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Linear Inverse Problems and Tikhonov Regularization by : Mark S. Gockenbach
Download or read book Linear Inverse Problems and Tikhonov Regularization written by Mark S. Gockenbach and published by American Mathematical Soc.. This book was released on 2016-12-31 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems occur frequently in science and technology, whenever we need to infer causes from effects that we can measure. Mathematically, they are difficult problems because they are unstable: small bits of noise in the measurement can completely throw off the solution. Nevertheless, there are methods for finding good approximate solutions. Linear Inverse Problems and Tikhonov Regularization examines one such method: Tikhonov regularization for linear inverse problems defined on Hilbert spaces. This is a clear example of the power of applying deep mathematical theory to solve practical problems. Beginning with a basic analysis of Tikhonov regularization, this book introduces the singular value expansion for compact operators, and uses it to explain why and how the method works. Tikhonov regularization with seminorms is also analyzed, which requires introducing densely defined unbounded operators and their basic properties. Some of the relevant background is included in appendices, making the book accessible to a wide range of readers.
Book Synopsis Convergence Rates of Approximate Least Squares Solutions of Linear Integral and Operator Equations of the First Kind by : M. Zuhair Nashed
Download or read book Convergence Rates of Approximate Least Squares Solutions of Linear Integral and Operator Equations of the First Kind written by M. Zuhair Nashed and published by . This book was released on 1973 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider approximations (x sub n) obtained by moment discretization to (i) the minimal (L sub 2)-norm solution of Kx = y where K is a Hilbert-Schmidt integral operator on (L sub 2), and to (ii) the least squares solution of minimal (L sub 2)-norm of the same equation when y is not in the range R(K) of K. (Modified author abstract).
Book Synopsis Numerical Methods For The Solution Of Linear Ill-Posed Problems by : Abdulaziz Mohammed M Alqahtani
Download or read book Numerical Methods For The Solution Of Linear Ill-Posed Problems written by Abdulaziz Mohammed M Alqahtani and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear ill-posed problems arise in various fields of science and engineering. Their solutions, if they exist, may not depend continuously on the observed data. To obtain stable approximate solutions, it is required to apply a regularization method. The main objective of this dissertation is to investigate regularization approaches and develop some numerical methods for solving problems of this kind. This work begins with an overview of linear ill-posed problems in continuous and discrete formulations. We review the most common regularization methods relying on some factorizations of the system matrix. Several iterative regularization strategies based on Krylov subspace methods are discussed, which are well-suited for solving large-scale problems. We then analyze the behavior of the symmetric block Lanczos method and the block Golub-Kahan bidiagonalization method when they are applied to the solution of linear discrete ill-posed problems. The analysis suggests that it generally is not necessary to compute the more expensive singular value decomposition when solving problems of this kind. The analysis of linear ill-posed problems often is carried out in function spaces using tools from functional analysis. The numerical solution of these problems typically is computed by first discretizing the problem and then applying tools from finite-dimensional linear algebra. We explore the feasibility of applying the Chebfun package to solve ill-posed problems with a regularize-first approach numerically. This allows a user to work with functions instead of vectors and with integral operators instead of matrices. The solution process is much closer to the analysis of ill-posed problems than standard linear algebra-based solution methods. The difficult process of explicitly choosing a suitable discretization is not required. The solution of linear ill-posed operator equations with the presence of errors in the operator and the data is discussed. An approximate solution of an ill-posed operator equation is obtained by first determining an approximation of the operators of generally fairly small dimension by carrying out a few steps of a continuous version of the Golub-Kahan bidiagonalization (GKB) process to the noisy operator. Then Tikhonov regularization is applied to the low-dimensional problem so obtained and the regularization parameter is determined by solving a low-dimensional nonlinear equation. The effect of replacing the original operator by the low-dimensional operator obtained by the GKB process on the accuracy of the solution is analyzed, as is the effect of errors in the operator and data.
Book Synopsis Government Reports Announcements by :
Download or read book Government Reports Announcements written by and published by . This book was released on 1973-08-10 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
