A Contemporary Study of Iterative Methods

A Contemporary Study of Iterative Methods

Convergence, Dynamics and Applications

1st Edition - February 13, 2018
This is the Latest Edition
  • Authors: A. Alberto Magrenan, Ioannis Argyros
  • Paperback ISBN: 9780128092149
  • eBook ISBN: 9780128094938

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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

Product details

  • No. of pages: 400
  • Language: English
  • Copyright: © Academic Press 2018
  • Published: February 13, 2018
  • Imprint: Academic Press
  • Paperback ISBN: 9780128092149
  • eBook ISBN: 9780128094938
  • 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