Topics in Iteration Theory
Author : György I. Targonski
Publisher :
Page : 304 pages
File Size : 32,90 MB
Release : 1981
Category : Iterative methods (Mathematics).
ISBN :
Author : György I. Targonski
Publisher :
Page : 304 pages
File Size : 32,90 MB
Release : 1981
Category : Iterative methods (Mathematics).
ISBN :
Author : W Forg-rob
Publisher : World Scientific
Page : 298 pages
File Size : 18,52 MB
Release : 1996-07-03
Category :
ISBN : 9814547891
Iteration theory has its roots in the operation of substituting functions into itself. This has led to questions like that of the behaviour of functions by repeating this substitution and when the number of iterations tends to infinity. The terms 'orbit' and 'chaos' appropriately describe this behaviour. Dynamical systems and the theory of functional equations play important roles in this field.
Author : Takanori Hida
Publisher :
Page : pages
File Size : 18,53 MB
Release : 2020
Category :
ISBN :
Author : Stephen L. Bloom
Publisher : Springer Science & Business Media
Page : 636 pages
File Size : 41,48 MB
Release : 2012-12-06
Category : Computers
ISBN : 3642780342
This monograph contains the results of our joint research over the last ten years on the logic of the fixed point operation. The intended au dience consists of graduate students and research scientists interested in mathematical treatments of semantics. We assume the reader has a good mathematical background, although we provide some prelimi nary facts in Chapter 1. Written both for graduate students and research scientists in theoret ical computer science and mathematics, the book provides a detailed investigation of the properties of the fixed point or iteration operation. Iteration plays a fundamental role in the theory of computation: for example, in the theory of automata, in formal language theory, in the study of formal power series, in the semantics of flowchart algorithms and programming languages, and in circular data type definitions. It is shown that in all structures that have been used as semantical models, the equational properties of the fixed point operation are cap tured by the axioms describing iteration theories. These structures include ordered algebras, partial functions, relations, finitary and in finitary regular languages, trees, synchronization trees, 2-categories, and others.
Author : Ioannis K. Argyros
Publisher : CRC Press
Page : 372 pages
File Size : 39,59 MB
Release : 2018-05-04
Category : Science
ISBN : 1351408976
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.
Author : Roman Liedl
Publisher : Springer
Page : 238 pages
File Size : 29,59 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 3540397493
Author : Stewart Levin
Publisher :
Page : 0 pages
File Size : 43,95 MB
Release : 1975
Category :
ISBN :
Author : Roman Liedl
Publisher :
Page : 244 pages
File Size : 33,10 MB
Release : 2014-01-15
Category :
ISBN : 9783662175057
Author : Kuflu Ghebremeskel
Publisher :
Page : 60 pages
File Size : 16,1 MB
Release : 1989
Category :
ISBN :
Author : Roman Liedl
Publisher : Springer
Page : 256 pages
File Size : 41,56 MB
Release : 1985
Category : Mathematics
ISBN :