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A Contemporary Study of Iterative Methods - 1st Edition - ISBN: 9780128092149, 9780128094938

A Contemporary Study of Iterative Methods

1st Edition

Convergence, Dynamics and Applications

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Authors: A. Alberto Magrenan Ioannis Argyros
Paperback ISBN: 9780128092149
eBook ISBN: 9780128094938
Imprint: Academic Press
Published Date: 16th February 2018
Page Count: 400
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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.

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


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

Table of Contents

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


No. of pages:
© Academic Press 2019
16th February 2018
Academic Press
Paperback ISBN:
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About the Authors

A. Alberto Magrenan

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.

Affiliations and Expertise

Department of Mathematics, Universidad Internacional de La Rioja, La Rioja, Spain

Ioannis Argyros

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.

Affiliations and Expertise

Department of Mathematical Sciences, Cameron University, Lawton, OK, USA


"“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

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