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Wednesday, July 22, 2020 | History

10 edition of Nonlinear Ill-posed Problems of Monotone Type found in the catalog.

Nonlinear Ill-posed Problems of Monotone Type

by Yakov Alber

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Published by Springer .
Written in English

    Subjects:
  • Mathematics,
  • Science/Mathematics,
  • Mathematical Analysis,
  • Linear Programming,
  • Number Systems,
  • Differential equations, Partial,
  • Improperly posed problems,
  • Mathematics / Mathematical Analysis,
  • Mathematics : Linear Programming,
  • Mathematics : Number Systems

  • The Physical Object
    FormatHardcover
    Number of Pages410
    ID Numbers
    Open LibraryOL8371850M
    ISBN 101402043953
    ISBN 109781402043956

    This book covers both the methods, including standard regularization theory, Fejer processes for linear and nonlinear problems, the balancing principle, extrapolated regularization, nonstandard regularization, nonlinear gradient method, the nonmonotone gradient   NONLINEAR ILL-POSED EQUATIONS 1. REPRESENTATION THEOREMS It is a well-known classical result that each compact linear operator T between Hilbert spaces has a representation with orthonormal systems (u,) and (II,,) and a positive monotone null sequence (A,,) TX = c &(x, u,) ~7,~ ( “=, especially

      2. Ill-posed problems 3. DSM for well-posed problems 4. DSM and linear ill-posed problems 5. Some inequalities 6. DSM for monotone operators 7. DSM for general nonlinear operator equations 8 DSM for operators satisfying a spectral assumption 9. DSM in Banach spaces DSM and Newton-type methods without inversion of the derivative DSM and Examples of inverse problems are image restoration and tomography, where one needs to improve blurred images or reconstruct pictures from raw data. This book describes new and existing numerical methods for the analysis and solution of rank-deficient and discrete ill-posed ://

    In this paper, we consider a multivariate spectral DY-type projection method for solving nonlinear monotone equations with convex constraints. The search direction of the proposed method combines those of the multivariate spectral gradient method and DY conjugate gradient method. With no need for the derivative information, the proposed method is very suitable to solve large-scale nonsmooth    Ill-posed problems on compact sets Ill-posed problems with sourcewise represented solutions Variational approach for constructing regularizing algorithms Nonlinear ill-posed problems Iterative and other methods References 3 Inverse


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Nonlinear Ill-posed Problems of Monotone Type by Yakov Alber Download PDF EPUB FB2

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 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,  › Mathematics › Analysis.

Nonlinear Ill-Posed Problems of Monotone Type 点击放大图片 出版社: Springer 作者: Alber, Yakov; Ryazantseva, Irina; Alber, Y.

出版时间: 年03月21 日 10位国际标准书号: 13位国际标准 Get this from a library. Nonlinear ill-posed problems of monotone type. [Yakov Alber; Irina Ryazantseva] -- "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 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. Rating: (not yet rated) 0 with reviews - Be the :// Buy Nonlinear Ill-posed Problems of Monotone Type on FREE SHIPPING on qualified orders   proved.

2 4 Nonlinear ill-posed problems with monotone operators There is a large literature on the equations () and () with monotone operators.

In the result we present the problem is nonlinear and ill-posed, the new technical tool, Theorem › 百度文库 › 行业资料. Problems from Another Time; Conference Calendar; Guidelines for Convergence Authors; MAA FOCUS; Math Horizons; Submissions to MAA Periodicals; Guide for Referees; MAA Press (an imprint of the AMS) MAA Notes; MAA Reviews.

Browse; MAA Library Recommendations; Additional Sources for Math Book Reviews; About MAA Reviews; Mathematical Communication Y. Alber and I. Ryazantseva, Nonlinear Ill-Posed Problems of Monotone Type, Springer, Dordrecht, [3] N.

Buong, Convergence rates in regularization for nonlinear ill-posed equations under accretive perturbations, ://?language=en. The authors propose an a-posteriors strategy for choosing the regularization parameter in Tikhonov regularization for solving nonlinear ill-posed problems and show that under certain conditions, the convergence rate obtained with this strategy is optimal.

As a by-product, a new stability estimate for the regularized solutions is given which applies to a class of parameter identification ://   We introduce a class of stabilizing Newton--Kaczmarz methods for nonlinear ill-posed problems and analyze their convergence and regularization behavior.

As usual for iterative methods for solving nonlinear ill-posed problems, conditions on the nonlinearity (or the derivatives) have to be imposed in order to obtain :// Nonlinear Ill-Posed Problems of Monotone Type 本类英文书关注排行 Technical Analysis of Stock Trends, Tenth Edition Differential Equations and Boundary Value Problems: Computing and Modeling Doing Math with Python Linear Algebra and its Applications Convergence rates of a penalized variational inequality method for nonlinear monotone ill-posed equations in Hilbert spaces Preprint (PDF Available) June with 66 Reads How we measure 'reads' With this book as their guide, readers will master the application of DSM to solve a variety of linear and nonlinear problems as well as ill-posed and well-posed :// The DSM for solving linear and nonlinear ill-posed problems in H consists of the construction of a dynamical system, that is, a Cauchy problem, which has the following properties: (1) it has a global solution, (2) this solution tends to a limit as time tends to infinity, (3) the limit solves the original linear or non-linear ?doi= JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS() Nonlinear Ill-Posed Equations: Singular Value Decomposition and the Picard Criterion EBERHARD SCHOCK Department of Mathematics, University of Kaiserslautern, Erwin Schringer-Strasse, Kaiserslautern, Federal Republic of Germany Submitted by Ky Fan The aim of this note is to discuss some basic Abstract.

The growth of the area of inverse problems within applied mathematics in recent years has been driven both by the needs of applications and by advances in a rigorous convergence theory of regularization methods for the solution of nonlinear ill-posed :// Nonlinear Ill Posed Problems of Monotone Type by Yakov Alber eBook: ISBN ISBN New not available: Used not available: Rentals not available: Digital not available: No copies of this book were found in stock from online book stores and marketplaces.

Alert me when this book becomes ://   for solving a very wide class of linear and nonlinear operator equations, especially ill-posed. There is a large literature on linear ill-posed problems (e.g. see 6), and a less extensive one on nonlinear ill-posed problems (e.g.

27, 10). Let us describe briefly the scope of the results obtained by the DSM in 10 —22, assuming (2) unless ~ramm/papers/pdf. Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems.

Usually the mathematical model of an inverse problem consists of an operator equation of the first kind and often the associated forward operator acts between Hilbert ://. Search by multiple ISBN, single ISBN, title, author, etc Login | Sign Up | Settings | Sell Books | Wish List: ISBN Actions: Add to Bookbag Sell This Book Add to Wish List Set Price Alert  In the book ”Operator theory and Applications”, Fields Institute Communica-tionsvol.

25, AMS,Providence,pp(, umar, s). Continuous Methods for Solving Nonlinear Ill-Posed Problems Ruben G. Airapetyan Department of Mathematics Kansas State University Manhattan, Kansas [email protected]://~ramm/papers/pdf.We study the convergence of the gradient descent method for solving ill-posed problems where the solution is characterized as a global minimum of a differentiable functional in a Hilbert space.

The classical least-squares functional for nonlinear operator equations is a special instance of this framework, and the gradient method then reduces to Landweber ://