
The Theory and Applications of Iteration Methods
CRC Press
Published on 4. May 2018
368 pages
978-1-351-40897-4 (ISBN)
System requirements
for ePUB without DRM
E-Book Single Licence
You are acquiring a single user licence for this eBook, which you might not transfer. [L]
Available for download
Description
Alles über E-Books | Antworten auf Fragen rund um E-Books, Kopierschutz und Dateiformate finden Sie in unserem Info- & Hilfebereich.
The Theory and Applications of Iteration Methods focuses on an abstract iteration scheme that consists of the recursive application of a point-to-set mapping. Each chapter presents new theoretical results and important applications in engineering, dynamic economic systems, and input-output systems. At the end of each chapter, case studies and numerical examples are presented from different fields of engineering and economics.
Following an outline of general iteration schemes, the authors extend the discrete time-scale Liapunov theory to time-dependent, higher order, nonlinear difference equations. The monotone convergence to the solution is examined in and comparison theorems are proven . Results generalize well-known classical theorems, such as the contraction mapping principle, the lemma of Kantorovich, the famous Gronwall lemma, and the stability theorem of Uzawa. The book explores conditions for the convergence of special single- and two-step methods such as Newton's method, modified Newton's method, and Newton-like methods generated by point-to-point mappings in a Banach space setting. Conditions are examined for monotone convergence of Newton's methods and their variants. Students and professionals in engineering, the physical sciences, mathematics, and economics will benefit from the book's detailed examples, step-by-step explanations, and effective organization.
Following an outline of general iteration schemes, the authors extend the discrete time-scale Liapunov theory to time-dependent, higher order, nonlinear difference equations. The monotone convergence to the solution is examined in and comparison theorems are proven . Results generalize well-known classical theorems, such as the contraction mapping principle, the lemma of Kantorovich, the famous Gronwall lemma, and the stability theorem of Uzawa. The book explores conditions for the convergence of special single- and two-step methods such as Newton's method, modified Newton's method, and Newton-like methods generated by point-to-point mappings in a Banach space setting. Conditions are examined for monotone convergence of Newton's methods and their variants. Students and professionals in engineering, the physical sciences, mathematics, and economics will benefit from the book's detailed examples, step-by-step explanations, and effective organization.
More details
Series
Language
English
Place of publication
London
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
Professional and scholarly
Product notice
Reflowable
Illustrations
3 Tables, black and white
File size
12,31 MB
ISBN-13
978-1-351-40897-4 (9781351408974)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions

Ioannis K. Argyros | Ferenc Szidarovszky
The Theory & Applications of Iteration Methods
Book
09/1993
1st Edition
CRC Press
€266.61
Article exhausted; check for reprint
Persons
Argyros, Ioannis K.; Szidarovszky, Ferenc
Content
The Convergence of Algorithmic Models. The Convergence of Iteration Sequences. Monotone Convergence. Comparison Theorems. The Convergence of Newton Methods and Their Variants. The Monotone Convergence of Newton Methods and Their Variants. References. Index.
System requirements
File format: ePUB
Copy protection: without DRM (Digital Rights Management)
System requirements:
- Computer (Windows; MacOS X; Linux): Use a reader that can handle the file format ePUB, such as Adobe Digital Editions or FBReader – both free (see eBook Help).
- Tablet/Smartphone (Android; iOS): Install the free app Adobe Digital Editions or the app PocketBook (see eBook Help).
- E-reader: Bookeen, Kobo, Pocketbook, Sony, Tolino and many more (not Kindle).
The file format ePUB works well for novels and non-fiction books – i.e., 'flowing' text without complex layout. On an e-reader or smartphone, line and page breaks automatically adjust to fit the small displays.
This eBook does not use copy protection or Digital Rights Management
For more information, see our eBook Help page.