Computational Theory of Iterative Methods

The book is designed for researchers, students and practitioners are interested in 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, in fact solutions of the equation. Problem 3: concerns the economy of the entire operations. Problem 4: concerns with how to choose a method, algorithm or software. The book includes applications in several areas of applied sciences including mathematical and mathematical economics. There is also a huge number of exercises complementing the theory.

- 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

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