Approximate Solution Of Operator Equations With Applications
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Approximate Solution Of Operator Equations With Applications
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Author : Ioannis K. Argyros
language : en
Publisher: World Scientific
Release Date : 2005
Approximate Solution Of Operator Equations With Applications written by Ioannis K. Argyros and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Researchers are faced with the problem of solving a variety of equations in the course of their work in engineering, economics, physics, and the computational sciences. This book focuses on a new and improved local-semilocal and monotone convergence analysis of efficient numerical methods for computing approximate solutions of such equations, under weaker hypotheses than in other works. This particular feature is the main strength of the book when compared with others already in the literature.The explanations and applications in the book are detailed enough to capture the interest of curious readers and complete enough to provide the necessary background material to go further into the subject.
Approximate Solutions Of Operator Equations
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Author : Mingjun Chen
language : en
Publisher: World Scientific
Release Date : 1997
Approximate Solutions Of Operator Equations written by Mingjun Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
This book offers an elementary and self-contained introduction to many fundamental issues concerning approximate solutions of operator equations formulated in an abstract Banach space setting, including important topics such as solvability, computational schemes, convergence, stability and error estimates. The operator equations under investigation include various linear and nonlinear types of ordinary and partial differential equations, integral equations, and abstract evolution equations, which are frequently involved in applied mathematics and engineering applications.Each chapter contains well-selected examples and exercises, for the purposes of demonstrating the fundamental theories and methods developed in the text and familiarizing the reader with functional analysis techniques useful for numerical solutions of various operator equations.
Approximate Solution Of Operator Equations With Applications
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Author : Ioannis K Argyros
language : en
Publisher: World Scientific Publishing Company
Release Date : 2005-08-26
Approximate Solution Of Operator Equations With Applications written by Ioannis K Argyros and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-26 with Mathematics categories.
Researchers are faced with the problem of solving a variety of equations in the course of their work in engineering, economics, physics, and the computational sciences. This book focuses on a new and improved local-semilocal and monotone convergence analysis of efficient numerical methods for computing approximate solutions of such equations, under weaker hypotheses than in other works. This particular feature is the main strength of the book when compared with others already in the literature.The explanations and applications in the book are detailed enough to capture the interest of curious readers and complete enough to provide the necessary background material to go further into the subject.
Linear Operator Equations Approximation And Regularization
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Author : M Thamban Nair
language : en
Publisher: World Scientific
Release Date : 2009-05-05
Linear Operator Equations Approximation And Regularization written by M Thamban Nair and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-05 with Mathematics categories.
Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not often be possible or may not be worth looking for due to physical constraints. In such situations, it is desirable to know how the so-called approximate solution approximates the exact solution, and what the error involved in such procedures would be.This book is concerned with the investigation of the above theoretical issues related to approximately solving linear operator equations. The main tools used for this purpose are basic results from functional analysis and some rudimentary ideas from numerical analysis. To make this book more accessible to readers, no in-depth knowledge on these disciplines is assumed for reading this book.
Approximate Solution Of Operator Equations
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Author : M.A. Krasnosel'skii
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Approximate Solution Of Operator Equations written by M.A. Krasnosel'skii and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
One of the most important chapters in modern functional analysis is the theory of approximate methods for solution of various mathematical problems. Besides providing considerably simplified approaches to numerical methods, the ideas of functional analysis have also given rise to essentially new computation schemes in problems of linear algebra, differential and integral equations, nonlinear analysis, and so on. The general theory of approximate methods includes many known fundamental results. We refer to the classical work of Kantorovich; the investigations of projection methods by Bogolyubov, Krylov, Keldysh and Petrov, much furthered by Mikhlin and Pol'skii; Tikho nov's methods for approximate solution of ill-posed problems; the general theory of difference schemes; and so on. During the past decade, the Voronezh seminar on functional analysis has systematically discussed various questions related to numerical methods; several advanced courses have been held at Voronezh Uni versity on the application of functional analysis to numerical mathe matics. Some of this research is summarized in the present monograph. The authors' aim has not been to give an exhaustive account, even of the principal known results. The book consists of five chapters.
Approximate Solution Of Operator Equations
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Author : M.A. Krasnosel'skii
language : en
Publisher: Springer
Release Date : 2011-11-20
Approximate Solution Of Operator Equations written by M.A. Krasnosel'skii and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-20 with Mathematics categories.
One of the most important chapters in modern functional analysis is the theory of approximate methods for solution of various mathematical problems. Besides providing considerably simplified approaches to numerical methods, the ideas of functional analysis have also given rise to essentially new computation schemes in problems of linear algebra, differential and integral equations, nonlinear analysis, and so on. The general theory of approximate methods includes many known fundamental results. We refer to the classical work of Kantorovich; the investigations of projection methods by Bogolyubov, Krylov, Keldysh and Petrov, much furthered by Mikhlin and Pol'skii; Tikho nov's methods for approximate solution of ill-posed problems; the general theory of difference schemes; and so on. During the past decade, the Voronezh seminar on functional analysis has systematically discussed various questions related to numerical methods; several advanced courses have been held at Voronezh Uni versity on the application of functional analysis to numerical mathe matics. Some of this research is summarized in the present monograph. The authors' aim has not been to give an exhaustive account, even of the principal known results. The book consists of five chapters.
Optimization Of Methods For Approximate Solution Of Operator Equations
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Author : Sergei V. Pereverzev
language : en
Publisher: Nova Science Publishers
Release Date : 1996
Optimization Of Methods For Approximate Solution Of Operator Equations written by Sergei V. Pereverzev and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
Approximate Solutions Of Operator Equations
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Author : Guanrong Chen
language : en
Publisher: World Scientific
Release Date : 1997-07-01
Approximate Solutions Of Operator Equations written by Guanrong Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-07-01 with Mathematics categories.
This book offers an elementary and self-contained introduction to many fundamental issues concerning approximate solutions of operator equations formulated in an abstract Banach space setting, including important topics such as solvability, computational schemes, convergence, stability and error estimates. The operator equations under investigation include various linear and nonlinear types of ordinary and partial differential equations, integral equations, and abstract evolution equations, which are frequently involved in applied mathematics and engineering applications.Each chapter contains well-selected examples and exercises, for the purposes of demonstrating the fundamental theories and methods developed in the text and familiarizing the reader with functional analysis techniques useful for numerical solutions of various operator equations.
Numerical Methods For The Solution Of Ill Posed Problems
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Author : A.N. Tikhonov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Numerical Methods For The Solution Of Ill Posed Problems written by A.N. Tikhonov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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. Non-existence and non-uniqueness can usually be overcome by settling for `generalised' solutions, leading to the need to develop regularising algorithms. The theory of ill-posed problems has advanced greatly since A. N. Tikhonov laid its foundations, the Russian original of this book (1990) rapidly becoming a classical monograph on the topic. The present edition has been completely updated to consider linear ill-posed problems with or without a priori constraints (non-negativity, monotonicity, convexity, etc.). 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 problems.
Methods And Applications Of Interval Analysis
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Author : Ramon E. Moore
language : en
Publisher: SIAM
Release Date : 1979-01-01
Methods And Applications Of Interval Analysis written by Ramon E. Moore and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-01-01 with Mathematics categories.
This book treats an important set of techniques that provide a mathematically rigorous and complete error analysis for computational results. It shows that interval analysis provides a powerful set of tools with direct applicability to important problems in scientific computing.