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Monday, April 27, 2020 | History

5 edition of Nonlinear Ill-Posed Problems (Applied Mathematics & Mathematical Computation) found in the catalog.

Nonlinear Ill-Posed Problems (Applied Mathematics & Mathematical Computation)

A.N. Tikhonov

Nonlinear Ill-Posed Problems (Applied Mathematics & Mathematical Computation)

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Published by Springer .
Written in English

    Subjects:
  • Mathematics,
  • Science/Mathematics,
  • Mathematical Analysis,
  • Applied mathematics,
  • Linear algebra,
  • Mathematics / Mathematical Analysis,
  • General

  • The Physical Object
    FormatHardcover
    Number of Pages424
    ID Numbers
    Open LibraryOL9896868M
    ISBN 100412759101
    ISBN 109780412759109
    OCLC/WorldCa39185960

    Continuous Methods for Well Posed Problems. Discretization Theorems for Well-posed Problems. An Non-linear Inequality. Regularization Procedure for Ill-posed Problems. Discretization Theorem for Ill-posed Problems. Regularized Continuous Methods for Monotone Operators. Regularized Discrete Methods for Monotone Operators. References.


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Nonlinear Ill-Posed Problems (Applied Mathematics & Mathematical Computation) by A.N. Tikhonov Download PDF EPUB FB2

Read While You Wait - Get immediate ebook access* when you order a print book Mathematics Nonlinear Ill-Posed Problems. Authors: Tikhonov, A.N. Buy this book Softco59 € price for Spain (gross) Buy Softcover ISBN ; Free shipping for individuals worldwide; Immediate ebook access* with your print order.

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. Nonlinear Ill-Posed Problems (Applied Mathematical Sciences) Softcover reprint of the original 1st ed. Edition by A.N. Tikhonov (Author) › Visit Amazon's A.N. Tikhonov Page. Find all the books, read about the author, and more.

See search results for this author. Are you an author. Cited by: Nonlinear ill-posed problems arise in a variety of important applications, ranging from medical imaging to geophysics to the nondestructive testing of materials.

This chapter provides an overview of the various numerical methods for nonlinear ill-posed problems. For each method, a.

Published in two volumes, this work introduces the reader to the theory of nonlinear ill-posed problems and its applications, and shows how to solve these problems using regularizing algorithms. There is an extensive bibliography on ill-posed and inverse problems.

: Nonlinear Ill-Posed Problems (Applied Mathematics & Mathematical Computation) (): Tikhonov, A.N.: Books1/5(1). This journal presents original articles on the theory, numerics and applications of inverse and ill-posed problems.

These inverse and ill-posed problems arise in mathematical physics and mathematical analysis, geophysics, acoustics, electrodynamics, tomography, medicine, ecology, financial mathematics etc. Articles on the construction and justification of new numerical algorithms of inverse.

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. Newton-type methods and in particular the Levenberg-Marquardt method for approximately solving smooth nonlinear ill-posed problems have been extensively investigated in Hilbert spaces; see, e.g.

SIAM Journal on Numerical AnalysisAbstract | PDF ( KB) () A multi-grid method with a priori and a posteriori level choice for the regularization of nonlinear ill-posed by: 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 Nonlinear Ill-Posed Problems book of monotone type in Hilbert and Banach spaces has grown rapidly over recent years.

Results. 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 Released on: Problems in nonlinear complex systems (so called chaotic systems) provide well-known examples of instability.

An ill-conditioned problem is indicated by a large condition number. If the problem is well-posed, then it stands a good chance of solution on a computer using a stable algorithm.

This paper discusses the inversion of nonlinear ill-posed problems. Such problems are solved through regularization and iteration and a major computational problem arises because the regularization parameter is not known a priori.

In this paper we show that the regularization should be made up of two parts. A global regularization parameter is required to deal with the measurement Cited by: An Overview of Numerical Methods for Nonlinear Ill-Posed Problems Curtis R.

Vogel Department of Mathematical Sciences Montana State University Bozeman, Montana I. INTRODUCTION Nonlinear ill-posed problems arise in a variety of important applications ranging from medical imaging to geophysics to the nondestructive testing of by: The notion of well- and ill-posed problems, and also that of problems intermediate between well- and ill-posed ones, is described.

Examples of such mathematical problems (systems of linear. 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.

() A new radial basis function for Helmholtz problems. Engineering Analysis with Boundary Elements() Optimization of image recording distances for quantitative X Cited by:   Inverse problems arise in practical applications whenever there is a need to interpret indirect measurements.

This book explains how to identify ill-posed inverse problems arising in practice and how to design computational solution methods for them; explains computational approaches in a hands-on fashion, with related codes available on a website; and serves as a convenient entry point to.

The second half of the book, perhaps with some additional readings, would be suitable for a more advanced graduate course on direct methods for the solution of nonlinear inverse problems. Brian Borchers is a professor of Mathematics at the New Mexico Institute of Mining and Technology.

These problems are typically ill-posed, in the sense that an arbitrarily small change in g can lead to an arbitrarily large change in the solution.

Contrast this to linear least squares problems on finite dimensional spaces, where the condition number of A provides a bound on the sensitivity of the solution of least squares problem to changes in b. Comments. The idea of conditional well-posedness was also found by B.L.

Phillips ; the expression "Tikhonov well-posed" is not widely used in the West. Other problems that lead to ill-posed problems in the sense described above are the Dirichlet problem for the wave equation, the non-characteristic Cauchy problem for the heat equation, the initial boundary value problem for the backwardheat.

Basic properties of regularization methods for linear ill-posed problems are studied by means of several simple analytical and numerical examples.

The second part of the book presents two special nonlinear inverse problems in detail - the inverse spectral problem and the inverse scattering : Shijun Liao. Dynamical Systems Method for Solving Nonlinear Operator Equations is of interest to graduate students in functional analysis, numerical analysis, and ill-posed and inverse problems especially.

The book presents a general method for solving operator equations, especially nonlinear and ill-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 problem.

INSTITUTE OF PHYSICS PUBLISHING INVERSE PROBLEMS Inverse Problems 19 () 1–21 PII: S(03) Tikhonov regularization and a posteriori rules for solving nonlinear ill posed problems UTautenhahn1 and Qi-nian Jin2 1 Department of Mathematics, University of Applied Sciences Zittau/Gorlitz, PO Box ,¨ Zittau, Germany 2 Department of Mathematics, Rutgers.

Nonlinear ill-posed problems, London: Chapman & Hall,2 vols. Applied mathematics and mathematical computation, v.

14, ISBN Publication Date: 00/ Adjoint Equations And Perturbation Algorithms In Nonlinear Problems. Welcome,you are looking at books for reading, the Adjoint Equations And Perturbation Algorithms In Nonlinear Problems, you will able to read or download in Pdf or ePub books and notice some of author may have lock the live reading for some of ore it need a FREE signup process to obtain the book.

Find many great new & used options and get the best deals for Inverse and Ill-Posed Problems: Inverse Problems for Kinetic and Other Evolution Equations 24 by Yu. Anikonov (, Hardcover) at the best online prices at eBay. Free shipping for many products. 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 treatme. Find many great new & used options and get the best deals for Radon Series on Computational and Applied Mathematics: Iterative Regularization Methods for Nonlinear Ill-Posed Problems 6 by Otmar Scherzer, Andreas Neubauer and Barbara Kaltenbacher (, Hardcover) at the best online prices at eBay.

Free shipping for many products. past two decades referring to some remarkable classes of ill-posed problems governed by non-accretive operators. All the results are derived from several compactness arguments, due mainly to the author, and are suitably illustrated by examples arising from various concrete problems - for example, nonlinear diffusion, heat conduction in.

Inverse and Ill-Posed Problems is a collection of papers presented at a seminar of the same title held in Austria in June The papers discuss inverse problems in various disciplines; mathematical solutions of integral equations of the first kind; general considerations for ill-posed problems; and the various regularization methods for integral and operator equations of the first Edition: 1.

您的位置: 首页 > 科学自然 > 数学 > Nonlinear Ill-Posed Problems 目录导航. 领导 创业 管理科学 特别兴趣. 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. We investigate iterated Tikhonov methods coupled with a Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations.

We show that the proposed method is a convergent regularization method. In the case of noisy data we propose a modification, the so called loping iterated Tikhonov-Kaczmarz method, where a sequence of relaxation parameters is introduced Cited by: Optimal experimental design (OED) of well-posed inverse problems is a well estab-lished field (e.g., Pukelsheim () and references therein) but, despite the practical necessity, experimental design of ill-posed inverse problems and in particular ill-posed nonlinear problems has remained largely unexplored.

We discuss some of the. Inv. Ill-Posed Problems16 (), – DOI / JIIP Definitions and examples of inverse and ill-posed problems S.

Kabanikhin Survey paper Abstract. The terms “inverse problems” and “ill-posed problems” have been steadily and surely gaining popularity in modern science since the middle of the 20th Size: KB. Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion Per Christian Hansen Here is an overview of modern computational stabilization methods for linear inversion, with applications to a variety of problems in audio processing, medical imaging, seismology, astronomy, and.

Nonlinear Ill-posed Problems of Monotone Type 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.

A regularization homotopy iterative method established for ill-posed nonlinear least squares problem. Two new regularization parameter selecting strategies are proposed, which are called direct search method and interval division method.

The calculation results of nonlinear least squares problems show that the regularization homotopy iterative method and parameter selecting strategies proposed Cited by: 5.The third part is devoted to ill-posed problems.

It can be read independently of the first two parts and presents a good example of applying the methods of calculus and functional analysis.

The first part "Basic Concepts" briefly introduces the language of set theory and concepts of .Compactness Methods for Nonlinear Evolutions - CRC Press Book This monograph provides a self-contained and comprehensive account of the most significant existence results obtained over thepast two decades referring to some remarkable classes of ill-posed .