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. - 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
Author(s): Ioannis K. Argyros (Eds.)
Series: Studies in computational mathematics 15
Edition: 1st ed
Publisher: Elsevier
Year: 2007
Language: English
Pages: 1-487
City: Amsterdam; London
Content:
Introduction
Pages vii-xi
Chapter 1 Linear spaces
Pages 1-15
Chapter 2 Monotone convergence
Pages 17-45
Chapter 3 Contractive fixed point theory
Pages 47-85
Chapter 4 Solving smooth equations
Pages 87-120
Chapter 5 Newton-like methods
Pages 121-186
Chapter 6 More results on Newton's method
Pages 187-244
Chapter 7 Equations wih nonsmooth operators
Pages 245-285
Chapter 8 Applications of the weaker version of the Newton-Kantorovich theorem
Pages 287-351
Chapter 9 The Newton-Kantorovich theorem and mathematical programming
Pages 353-378
Chapter 10 Generalized equations
Pages 379-407
Chapter 11 Monotone convergence of point to set-mapping
Pages 409-418
Chapter 12 Fixed points of point-to-set mappings
Pages 419-428
Chapter 13 Special topics
Pages 429-456
Bibliography
Pages 457-482
Appendix A Glossary of symbols
Page 483
Index
Pages 485-487
