Overview

A Contemporary Study of Iterative Methods: Convergence, Dynamics and Applications evaluates and compares advances in iterative techniques, also discussing their numerous applications in applied mathematics, engineering, mathematical economics, mathematical biology and other applied sciences. It uses the popular iteration technique in generating the approximate solutions of complex nonlinear equations that is suitable for aiding in the solution of advanced problems in engineering, mathematical economics, mathematical biology and other applied sciences. Iteration methods are also applied for solving optimization problems. In such cases, the iteration sequences converge to an optimal solution of the problem at hand.

Full Product Details

Author:   A. Alberto Magrenan (Department of Mathematics, Universidad Internacional de La Rioja, La Rioja, Spain) ,  Ioannis Argyros (Department of Mathematical Sciences, Cameron University, Lawton, OK, USA)
Publisher:   Elsevier Science Publishing Co Inc
Imprint:   Academic Press Inc
Weight:   0.450kg
ISBN:  

9780128092149

ISBN 10:   0128092149
Pages:   400
Publication Date:   16 February 2018
Audience:   College/higher education ,  Professional and scholarly ,  Tertiary & Higher Education ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

1. The majorization method in the Kantorovich theory 2. Directional Newton methods 3. Newton’s method 4. Generalized equations 5. Gauss–Newton method 6. Gauss–Newton method for convex optimization 7. Proximal Gauss–Newton method 8. Multistep modified Newton–Hermitian and Skew-Hermitian Splitting method 9. Secant-like methods in chemistry 10. Robust convergence of Newton’s method for cone inclusion problem 11. Gauss–Newton method for convex composite optimization 12. Domain of parameters 13. Newton’s method for solving optimal shape design problems 14. Osada method 15. Newton’s method to solve equations with solutions of multiplicity greater than one 16. Laguerre-like method for multiple zeros 17. Traub’s method for multiple roots 18. Shadowing lemma for operators with chaotic behavior 19. Inexact two-point Newton-like methods 20. Two-step Newton methods 21. Introduction to complex dynamics 22. Convergence and the dynamics of Chebyshev–Halley type methods 23. Convergence planes of iterative methods 24. Convergence and dynamics of a higher order family of iterative methods 25. Convergence and dynamics of iterative methods for multiple zeros

Reviews

""Contemporary in the title means that the coverage is state-of-the-art, with all currently-useful methods being shown. The level of detail is reasonable for an encyclopedia, and each chapter is extensively footnoted with references to research papers. Usually each chapter describes the method, quotes some theorems about the conditions under which it will succeed (occasionally with proofs), and usually a contrived numeric example to show how it works. There’s usually some discussion of convergence speed."" --MAA Reviews

Contemporary in the title means that the coverage is state-of-the-art, with all currently-useful methods being shown. The level of detail is reasonable for an encyclopedia, and each chapter is extensively footnoted with references to research papers. Usually each chapter describes the method, quotes some theorems about the conditions under which it will succeed (occasionally with proofs), and usually a contrived numeric example to show how it works. There's usually some discussion of convergence speed. --MAA Reviews

Contemporary in the title means that the coverage is state-of-the-art, with all currently-useful methods being shown. The level of detail is reasonable for an encyclopedia, and each chapter is extensively footnoted with references to research papers. Usually each chapter describes the method, quotes some theorems about the conditions under which it will succeed (occasionally with proofs), and usually a contrived numeric example to show how it works. There's usually some discussion of convergence speed. --MAA Reviews

Author Information

Professor Alberto Magreñán (Department of Mathematics, Universidad Internacional de La Rioja, Spain). Magreñán has published 43 documents. He works in operator theory, computational mathematics, Iterative methods, dynamical study and computation. 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.

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