This monograph provides a comprehensive study of both basic theory and new results in the area. Each chapter contains new theoretical results and importantapplications 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. 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 usedas a self-study reference or as a supplementary text for an advanced course in numerical functional analysis. Contains new theoretical results and important applications to engineering, dynamic economic systems, input-output systems,nonlinear and linear differential equations, and optimization problems Usefulto 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 INDICE: Preface.- Table of Contents.- 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.- Point-to-Set Mappings.- The Newton-Kantorovich Theorem and Mathematical Programming.- Glossary of Symbols.- Bibliography.
- ISBN: 978-0-387-72741-7
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 530
- Fecha Publicación: 01/06/2008
- Nº Volúmenes: 1
- Idioma: Inglés