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Convergence and Applications of Newton-type Iterations
ISBN-13:
9780387727431
Veröffentl:
2008
Seiten:
56
Autor:
Ioannis K. Argyros
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
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.
"This monograph is devoted to a comprehensive treatment of iterative methods for solving nonlinear equations with particular emphasis on semi-local 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 an advanced course on numerical functional analysis."
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.
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