Computational methods in nonlinear analysis : efficient algorithms, fixed point theory and applications / Ioannis K. Argyros, Said Hilout.

Format:

Book

Author/Creator:

Argyros, Ioannis K.

Contributor:

Hilout, Saïd.

Series:

Gale eBooks

Language:

English

Subjects (All):

Nonlinear theories--Data processing.

Nonlinear theories.

Mathematics--Data processing.

Mathematics.

Physical Description:

1 online resource (xv, 575 pages) : illustrations (some color)

Place of Publication:

Singapore ; Hackensack, N.J. : World Scientific, 2013.

Language Note:

English

Summary:

The field of computational sciences has seen a considerable development in mathematics, engineering sciences, and economic equilibrium theory. Researchers in this field are faced with the problem of solving a variety of equations or variational inequalities. We note that in computational sciences, the practice of numerical analysis for finding such solutions is essentially connected to variants of Newton's method. The efficient computational methods for finding the solutions of fixed points problems, nonlinear equations and variational inclusions are the first goal of the present book. The sec

Contents:

Preface; Contents; 1. Newton's Methods; 1.1 Convergence under Lipschitz Conditions; 1.2 Convergence under Generalized Lipschitz Conditions; 1.3 Convergence without Lipschitz Conditions; 1.4 Convex Majorants; 1.5 Nondiscrete Induction; 1.6 Exercises; 2. Special Conditions for Newton's Method; 2.1 ω*-Convergence; 2.2 Regular Smoothness; 2.3 Smale's α-Theory; 2.4 Exercises; 3. Newton's Method on Special Spaces; 3.1 Lie Groups; 3.2 Hilbert Space; 3.3 Convergence Structure; 3.4 Riemannian Manifolds; 3.5 Newton-type Method on Riemannian Manifolds; 3.6 Traub-type Method on Riemannian Manifolds

3.7 Exercises4. Secant Method; 4.1 Semi-local Convergence; 4.2 Secant-type Method and Nondiscrete Induction; 4.3 Efficient Secant-type Method; 4.4 Secant-like Method and Recurrent Functions; 4.5 Directional Secant-type Method; 4.6 A Unified Convergence Analysis; 4.7 Exercises; 5. Gauss-Newton Method; 5.1 Regularized Gauss-Newton Method; 5.2 Convex Composite Optimization; 5.3 Proximal Gauss-Newton Method; 5.4 Inexact Method and Majorant Conditions; 5.5 Exercises; 6. Halley's Method; 6.1 Semi-local Convergence; 6.2 Local Convergence; 6.3 Traub-type Multi point Method; 6.4 Exercises

7. Chebyshev's Method7.1 Directional Methods; 7.2 Chebyshev-Secant Methods; 7.3 Majorizing Sequences for Chebyshev's Method; 7.4 Exercises; 8. Broyden's Method; 8.1 Semi-local Convergence; 8.2 Exercises; 9. Newton-like Methods; 9.1 Modified Newton Method and Multiple Zeros; 9.2 Weak Convergence Conditions; 9.3 Local Convergence for Newton-type Method; 9.4 Two-step Newton-like Method; 9.5 A Unifying Semi-local Convergence; 9.6 High Order Traub-type Methods; 9.7 Relaxed Newton's Method; 9.8 Exercises; 10. Newton-Tikhonov Method for Ill-posed Problems

10.1 Newton-Tikhonov Method in Hilbert Space10.2 Two-step Newton-Tikhonov Method in Hilbert Space; 10.3 Regularization Methods; 10.4 Exercises; Bibliography; Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9789814405836

9814405833

OCLC:

855022917