A Contemporary Study of Iterative Methods
Convergence, Dynamics and Applications
Published on 16. February 2018
Book
Paperback/Softback
400 pages
978-0-12-809214-9 (ISBN)
Description
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.
Reviews / Votes
"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 ReviewsMore details
Language
English
Place of publication
San Diego
United States
Publishing group
Elsevier Science Publishing Co Inc
Target group
College/higher education
Professional and scholarly
Graduate students and some (appropriately skilled) senior undergraduate students, researchers and practitioners in applied and computational mathematics, optimization and related sciences requiring the solution to nonlinear equations situated in a scalar and an abstract domain.
Dimensions
Height: 229 mm
Width: 152 mm
Weight
450 gr
ISBN-13
978-0-12-809214-9 (9780128092149)
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
A. Alberto Magrenan | Ioannis Argyros
A Contemporary Study of Iterative Methods
Convergence, Dynamics and Applications
E-Book
02/2018
Academic Press
€72.99
Available for download
Persons
Professor Alberto Magrenan (Department of Mathematics, Universidad Internacional de La Rioja, Spain). Magrenan 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.
Content
1. The majorization method in the Kantorovich theory2. Directional Newton methods3. Newton's method4. Generalized equations5. Gauss-Newton method6. Gauss-Newton method for convex optimization7. Proximal Gauss-Newton method8. Multistep modified Newton-Hermitian and Skew-Hermitian Splitting method9. Secant-like methods in chemistry10. Robust convergence of Newton's method for cone inclusion problem11. Gauss-Newton method for convex composite optimization12. Domain of parameters13. Newton's method for solving optimal shape design problems14. Osada method15. Newton's method to solve equations with solutions of multiplicity greater than one16. Laguerre-like method for multiple zeros17. Traub's method for multiple roots18. Shadowing lemma for operators with chaotic behavior19. Inexact two-point Newton-like methods20. Two-step Newton methods21. Introduction to complex dynamics22. Convergence and the dynamics of Chebyshev-Halley type methods23. Convergence planes of iterative methods24. Convergence and dynamics of a higher order family of iterative methods25. Convergence and dynamics of iterative methods for multiple zeros