About the Book
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.
Readership 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
Quotes
"“Contemporary” in the title means that the coverage is stateoftheart, with all currentlyuseful 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
Content
1. The majorization method in the Kantorovich theory 2. Directional Newton methods 3. Newton’s method 4. Generalized equations 5. GaussNewton method 6. GaussNewton method for convex optimization 7. Proximal GaussNewton method 8. Multistep modified NewtonHermitian and SkewHermitian Splitting method 9. Secantlike methods in chemistry 10. Robust convergence of Newton’s method for cone inclusion problem 11. GaussNewton 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. Laguerrelike method for multiple zeros 17. Traub’s method for multiple roots 18. Shadowing lemma for operators with chaotic behavior 19. Inexact twopoint Newtonlike methods 20. Twostep Newton methods 21. Introduction to complex dynamics 22. Convergence and the dynamics of ChebyshevHalley 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
