A Contemporary Study of Iterative Methods: Convergence, Dynamics and Applications

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.

Contains recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spacesEncompasses the novel tool of dynamic analysis for iterative methods, including new developments in Smale stability theory and polynomiographyExplores the uses of computation of iterative methods across non-linear analysisUniquely places discussion of derivative-free methods in context of other discoveries, aiding comparison and contrast between options

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