The Theory and Applications of Iteration Methods

Released on by Ioannis K. Argyros
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  • The Theory and Applications of Iteration Methods Book Detail

  • Author : Ioannis K. Argyros
  • Release Date : 2018-05-04
  • Publisher : CRC Press
  • Genre : Science
  • Pages : 368
  • ISBN 13 : 1351408984
  • File Size : 39,39 MB
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The Theory and Applications of Iteration Methods by Ioannis K. Argyros PDF Summary

Book Description: 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.

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Iterative Methods for Linear Systems

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File Size : 82,82 MB
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Iterative Methods for Linear Systems?offers a mathematically rigorous introduction to fundamental iterative methods for systems of linear algebraic equations. T