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Computational methods in nonlinear analysis : efficient algorithms, fixed point theory and applications /
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, t...
| Clasificación: | Libro Electrónico |
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| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
[Hackensack] New Jersey :
World Scientific,
[2013]
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Argyros, Ioannis K., |e author. | |
| 245 | 1 | 0 | |a Computational methods in nonlinear analysis : |b efficient algorithms, fixed point theory and applications / |c Ioannis K. Argyros (Cameron University, USA), Saïd Hilout (Poitiers University, France). |
| 264 | 1 | |a [Hackensack] New Jersey : |b World Scientific, |c [2013] | |
| 264 | 4 | |c ©2013 | |
| 300 | |a 1 online resource (xv, 575 pages) | ||
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| 520 | |a 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 point problems, nonlinear equations and variational inclusions are the first goal of the present book. The second goal is the applications of these methods in nonlinear problems and the connection with fixed point theory. This book is intended for researchers in computational sciences, and as a reference book for an advanced computational methods in nonlinear analysis. We collect the recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces, and present several applications and connections with fixed point theory. The book contains abundant and updated bibliography, and provides comparison between various investigations made in recent years in the field of computational nonlinear analysis. | ||
| 504 | |a Includes bibliographical references (pages 553-572) and index. | ||
| 505 | 0 | |a 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. | |
| 588 | 0 | |a Print version record. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Nonlinear theories |x Data processing. | |
| 650 | 0 | |a Mathematics |x Data processing. | |
| 650 | 6 | |a Théories non linéaires |x Informatique. | |
| 650 | 6 | |a Mathématiques |x Informatique. | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x General. |2 bisacsh | |
| 650 | 7 | |a Mathematics |x Data processing |2 fast | |
| 650 | 7 | |a Nonlinear theories |x Data processing |2 fast | |
| 700 | 1 | |a Hilout, Saïd, |e author. | |
| 776 | 0 | 8 | |i Print version: |a Argyros, Ioannis K. |t Computational methods in nonlinear analysis. |d New Jersey : World Scientific, [2013] |z 9789814405829 |w (DLC) 2013005325 |w (OCoLC)792884975 |
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