Iterative Methods and Their Dynamics with Applications : a Contemporary Study.
Iterative processes are the tools used to generate sequences approximating solutions of equations describing real life problems. Intended for researchers in computational sciences and as a reference book for advanced computational method in nonlinear analysis, this book is a collection of the recent...
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| Format: | eBook |
| Language: | English |
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Portland :
CRC Press,
2017.
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| Online Access: | Connect to the full text of this electronic book |
| Summary: | Iterative processes are the tools used to generate sequences approximating solutions of equations describing real life problems. Intended for researchers in computational sciences and as a reference book for advanced computational method in nonlinear analysis, this book is a collection of the recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces and presents several applications and connections with fixed point theory. It contains an abundant and updated bibliography and provides comparisons between various investigations made in recent years in the field of computational nonlinear analysis. The book also provides recent advancements in the study of iterative procedures and can be used as a source to obtain the proper method to use in order to solve a problem. The book assumes a basic background in Mathematical Statistics, Linear Algebra and Numerical Analysis and may be used as a self-study reference or as a supplementary text for an advanced course in Biosciences or Applied Sciences. Moreover, the newest techniques used to study the dynamics of iterative methods are described and used in the book and they are compared with the classical ones. |
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| Physical Description: | 1 online resource (366 pages) |
| Bibliography: | References-Chapter 16 Generalized Newton method with applications-16.1 Introduction-16.2 Preliminaries-16.3 Semilocal convergence-References-Chapter 17 Newton-secant methods with values in a cone-17.1 Introduction-17.2 Convergence of the Newton-secant method-References-Chapter 18 Gauss-Newton method with applications to convex optimization-18.1 Introduction-18.2 Gauss-Newton Algorithm and Quasi-Regularity condition-18.2.1 Gauss-Newton Algorithm GNA-18.2.2 Quasi Regularity-18.3 Semilocal convergence for GNA-18.4 Specializations and numerical examples-References-Chapter 19 Directional Newton methods and restricted domains-19.1 Introduction-19.2 Semilocal convergence analysis-References-Chapter 20 Expanding the applicability of the Gauss-Newton method for convex optimization under restricted convergence domains and majorant conditions-20.1 Introduction-20.2 Gauss-Newton Algorithm and Quasi-Regularity condition-20.2.1 Gauss-Newton Algorithm GNA-20.2.2 Quasi Regularity-20.3 Semi-local convergence-20.4 Numerical examples-References-Chapter 21 Ball Convergence for eighth order method-21.1 Introduction-21.2 Local convergence analysis-21.3 Numerical examples-References-Chapter 22 Expanding Kantorovich's theorem for solving generalized equations-22.1 Introduction-22.2 Preliminaries-22.3 Semilocal convergence-References-Index. |
| ISBN: | 9781498763622 1498763626 9781351649506 1351649507 1315153467 9781315153469 |