A Contemporary Study of Iterative Methods Convergence, Dynamics and Applications

Langue : Anglais

Auteurs : Magrenan A. Alberto, Argyros Ioannis

Couverture de l’ouvrage A Contemporary Study of Iterative Methods

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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.

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

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.

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.

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