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Monday, May 11, 2020 | History

6 edition of Numerical methods for the solution of ill-posed problems found in the catalog.

Numerical methods for the solution of ill-posed problems

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Published by Kluwer Academic Publishers in Dordrecht, Boston .
Written in English

    Subjects:
  • Numerical analysis -- Improperly posed problems,
  • Numerical analysis -- Improperly posed problems -- Data processing

  • Edition Notes

    Includes bibliographical references (p. 239-251) and index.

    Statementby A.N. Tikhonov ... [et al.].
    SeriesMathematics and its applications ;, v. 328, Mathematics and its applications (Kluwer Academic Publishers) ;, v. 328.
    ContributionsTikhonov, A. N. 1906-
    Classifications
    LC ClassificationsQA297 .C48313 1995
    The Physical Object
    Paginationix, 253 p. :
    Number of Pages253
    ID Numbers
    Open LibraryOL789234M
    ISBN 10079233583X
    LC Control Number95021648

    Buy Numerical Methods for the Solution of Ill-Posed Problems (Mathematics and Its Applications (closed)) Softcover reprint of hardcover 1st ed. by A.N. Tikhonov (ISBN: ) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders. Solution Manual for Numerical Methods for Engineers 7th Edition by Chapra. Full file at

    The main classes of inverse problems for equations of mathematical physics and their numerical solution methods are considered in this book which is intended for graduate students and experts in applied mathematics, computational mathematics, and mathematical modelling. Such problems are called essentially ill-posed. An approach has been worked out to solve ill-posed problems that makes it possible to construct numerical methods that approximate solutions of essentially ill-posed problems of the form \ref{eq1} which are stable under small changes of the data.

    Download Numerical Methods By Rao V. Dukkipati – Numerical Methods book is designed as an introductory undergraduate or graduate course for mathematics, science and engineering students of all text covers all major aspects of numerical methods, including numerical computations, matrices and linear system of equations, solution of algebraic and transcendental equations, finite. 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 problems.


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Numerical methods for the solution of ill-posed problems Download PDF EPUB FB2

Many problems in science, technology and engineering are posed in the form of operator equations of the first kind, with the operator and RHS approximately known.

But such problems often turn out to be ill-posed, having no solution, or a non-unique solution, and/or an unstable solution.

Numerical Methods for the Solution of Ill-Posed Problems (Mathematics and Its Applications): Tikhonov, A.N., Goncharsky, A., Stepanov, V.V., Yagola, Anatoly G.: : by: Numerical Methods for the Solution of Ill-Posed Problems.

Many problems in science, technology and engineering are posed in the form of operator equations of the first kind, with the operator and RHS approximately known.

But such problems often turn out to be ill-posed, having no solution, or a non-unique solution, and/or an unstable solution. Besides the theoretical material, the book also contains a FORTRAN program library.

Audience: Postgraduate students of physics, mathematics, chemistry, economics, engineering. Engineers and scientists interested in data processing and the theory of ill-posed : $ Numerical Methods for the Solution of Ill-Posed Problems - A.N.

Tikhonov, A. Goncharsky, V.V. Stepanov, Anatoly G. Yagola - Google Books. Many problems in science, technology and engineering are posed in the form of operator equations of the first kind, with the operator and RHS approximately known.

But such problems often turn out to be ill-posed, having no solution, or a non-unique. Buy Numerical Methods for Solving Inverse Problems of Mathematical Physics (Inverse and Ill-Posed Problems) on FREE SHIPPING on qualified orders Numerical Methods for Solving Inverse Problems of Mathematical Physics (Inverse and Ill-Posed Problems): Vabishchevich, Petr N., Samarskii, A.

A.: : BooksCited by: Numerical methods for the solution of ill-posed problems Numerical methods for the solution of ill-posed problems by A. Tikhonov Published by Kluwer Academic Publishers in Pages: Numerical methods for the solution of ill-posed problems.

[A N Tikhonov;] -- Many problems in science, technology, and engineering are posed in the form of operator equations of the first kind with the operator and right part approximately known. Numerical methods for the approximate Solution of ill-posed problems on compact sets 65 1.

Approximate Solution of ill-posed problems on compact sets 66 2. Some theorems regarding uniform approximation to the exact So­ lution of ill-posed problems 67 3. Some theorems about convex polyhedra in R™ 70 4. Such problems arise for example in the regularization of ill-posed problems in image restoration where, in addition, some of the matrices involved are very ill-conditioned.

The new method uses recently developed techniques for the large-scale trust-region subproblem. Preface to the English edition.

Introduction. Regularization methods. Numerical methods for the approximate solution of ill-posed problems on compact sets. Algorithms for the approximate solution of ill-posed problems on special sets.

Algorithms and programs for solving linear ill-posed problems. Appendix: Program listings. The mollification method and the numerical solution of ill-posed problems / by Diego A.

Murio. "A Wiley interscience publication." Includes bibliographical references and index. ISBN 1. Inverse problems (Differential equations)—Improperly posed problems. Inverse problems (Differential equations)—Numerical solutions File Size: KB.

For the latter purpose this book provides stimulating concepts and methods that have no nontrivial counterpart in mathematical analysis of well-posed problems. As far as methods of constructing solutions that are easily processed on a computer, this monograph represents the history, and not the future of numerical analysis of ill-posed problems.

"The book is very carefully written, in a reader-friendly style. It can be considered as an introductory textbook for the theory of ill-posed problems and their numerical solution." (Mathematical Reviews/MathSciNet 11/05/).

Design/methodology/approach A numerical method based on the finite-difference scheme and the least squares approach for numerical solution of the direct and inverse problems has been recently. But such problems often turn out to be ill-posed, having no solution, or a non-unique solution, and/or an unstable solution.

Non-existence and non-uniqueness can usually be overcome by settling for 'generalised' solutions, leading to the need to develop regularising algorithms. This book describes, in a common framework, new and existing numerical methods for the analysis and solution of rank-deficient and discrete ill-posed problems.

The emphasis is on insight into the stabilizing properties of the algorithms and on the efficiency and reliability of the computations. Numerical Methods: Problems and Solutions By M.K.

Jain, S. Iyengar, R. Jain – Numerical Methods is an outline series containing brief text of numerical solution of transcendental and polynomial equations, system of linear algebraic equations and eigenvalue problems, interpolation and approximation, differentiation and integration, ordinary differential equations and complete.

The introductory chapter describes the two types of problems (rank-deficient and discrete ill-posed), including an explanation of how discrete ill-posed arise from integral equation problems. It also presents four test problems that are used throughout the book as examples of the methods introduced.

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. Solution of Ill-Posed Problems by Means of Truncated SVD. Numerical Mathematics Singapore() The truncatedSVD as a method for by: Abstract.

In Chapter 2 we have succeeded in solving, in a number of cases, the first problem posed to us: starting from qualitative information regarding the unknown solution, how to find the compact set of well-posedness M containing the exact solution.

It was shown that this can be readily done if the exact solution of the problem belongs to Z↓ C, Ž C, Ž↓ : A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, A. G. Yagola.Numerical methods vary in their behavior, and the many different types of differ-ential equation problems affect the performanceof numerical methods in a variety of ways.

An excellent book for “real world” examples of solving differential equations is that of Shampine, Gladwell, and Thompson [74].File Size: 1MB.