A Contemporary Study of Iterative Methods
Convergence, Dynamics and Applications
- 1st Edition - February 13, 2018
- Latest edition
- Authors: A. Alberto Magrenan, Ioannis Argyros
- Language: English
A Contemporary Study of Iterative Methods: Convergence, Dynamics and Applications evaluates and compares advances in iterative techniques, also discussing their numerous applicati… Read more
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Description
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.
Key features
Key features
- Contains recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces
- Encompasses the novel tool of dynamic analysis for iterative methods, including new developments in Smale stability theory and polynomiography
- Explores the uses of computation of iterative methods across non-linear analysis
- Uniquely places discussion of derivative-free methods in context of other discoveries, aiding comparison and contrast between options
Readership
Readership
Table of contents
Table of contents
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
Review quotes
Review quotes
"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
Product details
Product details
- Edition: 1
- Latest edition
- Published: February 16, 2018
- Language: English
About the authors
About the authors
AM
A. Alberto Magrenan
IA