The book is designed for researchers, students and practitioners interested in using fast and efficient iterative methods to approximate solutions of nonlinear equations. The following four major problems are addressed. Problem 1: Show that the iterates are well defined. Problem 2: concerns the convergence of the sequences generated by a process and the question of whether the limit points are, in fact solutions of the equation. Problem 3: concerns the economy of the entire operations. Problem 4: concerns with how to best choose a method, algorithm or software program to solve a specific type of problem and its description of when a given algorithm succeeds or fails. The book contains applications in several areas of applied sciences including mathematical programming and mathematical economics. There is also a huge number of exercises complementing the theory.

Key Features

- Latest convergence results for the iterative methods - Iterative methods with the least computational cost - Iterative methods with the weakest convergence conditions - Open problems on iterative methods


Primary market(s): Researchers in the USA Secondary market(s): Researchers in Western Europe, South Korea & Japan

Table of Contents

1. Linear Spaces 2. Monotone convergence 3. Contractive Fixed Point Theory 4. Solving Smooth Equations 5. Newton-like methods 6. More Results on Newton's Method 7. Equations with Nonsmooth Operators 8. Applications of the weaker version of the Newton-Kantorovich theorem 9. The Newton-Kantorovich Theorem and Mathematical Programming 10. Generalized equations 11. Monotone convergence of point to set-mapping 12. Fixed points of point-to-set mappings 13. Special topics Bibliography A Glossary of Symbols Index


No. of pages:
© 2007
Elsevier Science
eBook ISBN:
Print ISBN:

About the author

Ioannis Argyros

Affiliations and Expertise

Department of Mathematical Sciences Cameron University, Lawton, OK, USA