The Theory and Applications of Iteration Methods (Systems Engineering Ser. #4)

Synopsis

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.

Copyright:

1993

Book Details

Book Quality:

Publisher Quality

Book Size:

368 Pages

ISBN-13:

9781351408974

Related ISBNs:

9780849380143, 9780203719169

Publisher:

CRC Press

Date of Addition:

09/24/23

Copyrighted By:

Ioannis K. Argyros, Ferenc Szidarovszky

Adult content:

No

Language:

English

Has Image Descriptions:

No

Categories:

Nonfiction, Technology, Earth Sciences, Mathematics and Statistics

Submitted By:

Bookshare Staff

Usage Restrictions:

This is a copyrighted book.