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...
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| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
[Hackensack] New Jersey :
World Scientific,
[2013]
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (xv, 575 pages) |
| Bibliographie: | Includes bibliographical references (pages 553-572) and index. |
| ISBN: | 9789814405836 9814405833 |
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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. | |
| 650 | 0 | |a Nonlinear theories |x Data processing. | |
| 650 | 0 | |a Mathematics |x Data processing. |0 http://id.loc.gov/authorities/subjects/sh85082146 | |
| 650 | 6 | |a Théories non linéaires |x Informatique. | |
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| author | Argyros, Ioannis K. Hilout, Saïd |
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| 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. |
| ctrlnum | (OCoLC)855022917 |
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| dewey-ones | 515 - Analysis |
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| dewey-search | 515/.355 |
| dewey-sort | 3515 3355 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:28Z |
| institution | BVB |
| isbn | 9789814405836 9814405833 |
| language | English |
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| publisher | World Scientific, |
| record_format | marc |
| spelling | Argyros, Ioannis K., author. Computational methods in nonlinear analysis : efficient algorithms, fixed point theory and applications / Ioannis K. Argyros (Cameron University, USA), Saïd Hilout (Poitiers University, France). [Hackensack] New Jersey : World Scientific, [2013] ©2013 1 online resource (xv, 575 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier 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. Includes bibliographical references (pages 553-572) and index. 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. Print version record. Nonlinear theories Data processing. Mathematics Data processing. http://id.loc.gov/authorities/subjects/sh85082146 Théories non linéaires Informatique. Mathématiques Informatique. MATHEMATICS Differential Equations General. bisacsh Mathematics Data processing fast Nonlinear theories Data processing fast Hilout, Saïd, author. has work: Computational methods in nonlinear analysis (Text) https://id.oclc.org/worldcat/entity/E39PCFFVbMRR6bDRq9mDV77pGd https://id.oclc.org/worldcat/ontology/hasWork Print version: Argyros, Ioannis K. Computational methods in nonlinear analysis. New Jersey : World Scientific, [2013] 9789814405829 (DLC) 2013005325 (OCoLC)792884975 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=622027 Volltext |
| spellingShingle | Argyros, Ioannis K. Hilout, Saïd Computational methods in nonlinear analysis : efficient algorithms, fixed point theory and applications / 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. Nonlinear theories Data processing. Mathematics Data processing. http://id.loc.gov/authorities/subjects/sh85082146 Théories non linéaires Informatique. Mathématiques Informatique. MATHEMATICS Differential Equations General. bisacsh Mathematics Data processing fast Nonlinear theories Data processing fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85082146 |
| title | Computational methods in nonlinear analysis : efficient algorithms, fixed point theory and applications / |
| title_auth | Computational methods in nonlinear analysis : efficient algorithms, fixed point theory and applications / |
| title_exact_search | Computational methods in nonlinear analysis : efficient algorithms, fixed point theory and applications / |
| title_full | Computational methods in nonlinear analysis : efficient algorithms, fixed point theory and applications / Ioannis K. Argyros (Cameron University, USA), Saïd Hilout (Poitiers University, France). |
| title_fullStr | Computational methods in nonlinear analysis : efficient algorithms, fixed point theory and applications / Ioannis K. Argyros (Cameron University, USA), Saïd Hilout (Poitiers University, France). |
| title_full_unstemmed | Computational methods in nonlinear analysis : efficient algorithms, fixed point theory and applications / Ioannis K. Argyros (Cameron University, USA), Saïd Hilout (Poitiers University, France). |
| title_short | Computational methods in nonlinear analysis : |
| title_sort | computational methods in nonlinear analysis efficient algorithms fixed point theory and applications |
| title_sub | efficient algorithms, fixed point theory and applications / |
| topic | Nonlinear theories Data processing. Mathematics Data processing. http://id.loc.gov/authorities/subjects/sh85082146 Théories non linéaires Informatique. Mathématiques Informatique. MATHEMATICS Differential Equations General. bisacsh Mathematics Data processing fast Nonlinear theories Data processing fast |
| topic_facet | Nonlinear theories Data processing. Mathematics Data processing. Théories non linéaires Informatique. Mathématiques Informatique. MATHEMATICS Differential Equations General. Mathematics Data processing Nonlinear theories Data processing |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=622027 |
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