Computational Theory of Iterative Methods - 1st Edition - ISBN: 9780444531629, 9780080560700

Computational Theory of Iterative Methods, Volume 15

1st Edition

Authors: Ioannis Argyros
eBook ISBN: 9780080560700
Hardcover ISBN: 9780444531629
Imprint: Elsevier Science
Published Date: 4th September 2007
Page Count: 504
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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

Description

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

Readership

Primary market(s): Researchers in the USA

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


Details

No. of pages:
504
Language:
English
Copyright:
© Elsevier Science 2007
Published:
Imprint:
Elsevier Science
eBook ISBN:
9780080560700
Hardcover ISBN:
9780444531629

About the Authors

Ioannis Argyros Author

Professor Ioannis Argyros (Department of Mathematical Sciences Cameron University, Lawton, OK, USA) has published 329 indexed documents and 25 books. Argyros is interested in theories of inequalities, operators, computational mathematics and iterative methods, and banach spaces.

Affiliations and Expertise

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