Details
Convergence and Applications of Newton-type Iterations
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53,49 € |
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| Verlag: | Springer |
| Format: | |
| Veröffentl.: | 12.06.2008 |
| ISBN/EAN: | 9780387727431 |
| Sprache: | englisch |
| Anzahl Seiten: | 56 |
Dieses eBook enthält ein Wasserzeichen.
Beschreibungen
<P>Recent results in local convergence and semi-local convergence analysis constitute a natural framework for the theoretical study of iterative methods. This monograph provides a comprehensive study of both basic theory and new results in the area. Each chapter contains new theoretical results and important applications in engineering, modeling dynamic economic systems, input-output systems, optimization problems, and nonlinear and linear differential equations. Several classes of operators are considered, including operators without Lipschitz continuous derivatives, operators with high order derivatives, and analytic operators. Each section is self-contained. Examples are used to illustrate the theory and exercises are included at the end of each chapter.</P>
<P>The book assumes a basic background in linear algebra and numerical functional analysis. Graduate students and researchers will find this book useful. It may be used as a self-study reference or as a supplementary text for an advanced course in numerical functional analysis.</P>
<P>The book assumes a basic background in linear algebra and numerical functional analysis. Graduate students and researchers will find this book useful. It may be used as a self-study reference or as a supplementary text for an advanced course in numerical functional analysis.</P>
Operators and Equations.- The Newton Kantorovich (NK) Method.- Applications of the Weaker Version of the NK Theorem.- Special Methods.- Newton-like Methods.- Analytic Computational Complexity We Are Concerned with the Choice of Initial Approximations.- Variational Inequalities.- Convergence Involving Operators with Outer or Generalized Inverses.- Convergence on Generalized Banach Spaces: Improving Error Bounds and Weakening of Convergence Conditions.- Point to Set Mappings.- The Newton Kantorovich Theorem and Mathematical Programming.
<P>Recent results in local convergence and semi-local convergence analysis constitute a natural framework for the theoretical study of iterative methods. This monograph provides a comprehensive study of both basic theory and new results in the area. Each chapter contains new theoretical results and important applications in engineering, modeling dynamic economic systems, input-output systems, optimization problems, and nonlinear and linear differential equations. Several classes of operators are considered, including operators without Lipschitz continuous derivatives, operators with high order derivatives, and analytic operators. Each section is self-contained. Examples are used to illustrate the theory and exercises are included at the end of each chapter.</P>
<P>The book assumes a basic background in linear algebra and numerical functional analysis. Graduate students and researchers will find this book useful. It may be used as a self-study reference or as a supplementary text for an advanced course in numerical functional analysis.</P>
<P>The book assumes a basic background in linear algebra and numerical functional analysis. Graduate students and researchers will find this book useful. It may be used as a self-study reference or as a supplementary text for an advanced course in numerical functional analysis.</P>
An ideal introduction to the field Contains new theoretical results and important applications to engineering, dynamic economic systems, input-output systems, nonlinear and linear differential equations, and optimization problems Useful to an audience of graduate students and researchers working in the areas of numerical and functional analysis or computer science Includes many solved problems and exercises at the end of each chapter Includes supplementary material: sn.pub/extras
<P>This monograph is devoted to a comprehensive treatment of iterative methods for solving nonlinear equations with particular emphasis on semilocal convergence analysis. Theoretical results are applied to engineering, dynamic economic systems, input-output systems, nonlinear and linear differential equations, and optimization problems. Accompanied by many exercises, some with solutions, the book may be used as a supplementary text in the classroom for seminars in advanced numerical and functional analysis or computer science.</P>
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