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Computational methods in nonlinear analysis : efficient algorithms, fixed point theory and applications

Author: Ioannis K Argyros; Saïd Hilout
Publisher: [Hackensack] New Jersey : World Scientific, [2013] ©2013
Edition/Format:   eBook : Document : EnglishView all editions and formats
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.  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Argyros, Ioannis K.
Computational methods in nonlinear analysis.
New Jersey : World Scientific, [2013]
(DLC) 2013005325
(OCoLC)792884975
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Ioannis K Argyros; Saïd Hilout
ISBN: 9789814405836 9814405833
OCLC Number: 855022917
Description: 1 online resource (xv, 575 pages)
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. [symbol]-convergence. 2.2. Regular smoothness. 2.3. Smale's [symbol]-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. Exercises --
4. 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 multipoint method. 6.4. Exercises --
7. Chebyshev's method. 7.1. 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 space. 10.2. Two-step Newton-Tikhonov method in Hilbert space. 10.3. Regularization methods. 10.4. Exercises.
Responsibility: Ioannis K. Argyros (Cameron University, USA), Saïd Hilout (Poitiers University, France).

Abstract:

Suitable for researchers in computational sciences and advanced computational methods in nonlinear analysis, this title provides the results on the convergence analysis of numerical algorithms in  Read more...

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