Convergence and Applications of Newton-type Iterations

This book presents iterative methods for solving nonlinear equations. It applies theoretical results to engineering, dynamic economic systems, input-output systems, nonlinear and linear differential equations, and optimization problems.

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.

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

Inhalt
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.