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Argyros I.K. Convergence and Applications of Newton-type Iterations

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Argyros I.K. Convergence and Applications of Newton-type Iterations
New York: Springer, 2008. — 512 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.
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.
Contents :

Front Matter
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
Back Matter
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