Multipoint Methods For Solving Nonlinear Equations
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Multipoint Methods For Solving Nonlinear Equations
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Author : Miodrag Petković
language : en
Publisher:
Release Date : 2013
Multipoint Methods For Solving Nonlinear Equations written by Miodrag Petković and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Differential equations, Nonlinear categories.
This book is the first on the topic and explains the most cutting-edge methods needed for precise calculations and explores the development of powerful algorithms to solve research problems. Multipoint methods have an extensive range of practical applications significant in research areas such as signal processing, analysis of convergence rate, fluid mechanics, solid state physics, and many others. The book takes an introductory approach in making qualitative comparisons of different multipoint methods from various viewpoints to help the reader understand applications of more complex methods. Evaluations are made to determine and predict efficiency and accuracy of presented models useful to wide a range of research areas along with many numerical examples for a deep understanding of the usefulness of each method. This book will make it possible for the researchers to tackle difficult problems and deepen their understanding of problem solving using numerical methods. Multipoint methods are of great practical importance, as they determine sequences of successive approximations for evaluative purposes. This is especially helpful in achieving the highest computational efficiency. The rapid development of digital computers and advanced computer arithmetic have provided a need for new methods useful to solving practical problems in a multitude of disciplines such as applied mathematics, computer science, engineering, physics, financial mathematics, and biology. Provides a succinct way of implementing a wide range of useful and important numerical algorithms for solving research problems Illustrates how numerical methods can be used to study problems which have applications in engineering and sciences, including signal processing, and control theory, and financial computation Facilitates a deeper insight into the development of methods, numerical analysis of convergence rate, and very detailed analysis of computational efficiencyProvides a powerful means of learning by systematic experimentation with some of the many fascinating problems in scienceIncludes highly efficient algorithms convenient for the implementation into the most common computer algebra systems such as Mathematica, MatLab, and Maple.
Iterative Methods For Solving Nonlinear Equations And Systems
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Author : Juan R. Torregrosa
language : en
Publisher: MDPI
Release Date : 2019-12-06
Iterative Methods For Solving Nonlinear Equations And Systems written by Juan R. Torregrosa and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-06 with Mathematics categories.
Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a non-trivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.
Multipoint Methods For Solving Nonlinear Equations
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Author : Miodrag Petkovic
language : en
Publisher: Academic Press
Release Date : 2012-12-31
Multipoint Methods For Solving Nonlinear Equations written by Miodrag Petkovic and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-31 with Technology & Engineering categories.
This book is the first on the topic and explains the most cutting-edge methods needed for precise calculations and explores the development of powerful algorithms to solve research problems. Multipoint methods have an extensive range of practical applications significant in research areas such as signal processing, analysis of convergence rate, fluid mechanics, solid state physics, and many others. The book takes an introductory approach in making qualitative comparisons of different multipoint methods from various viewpoints to help the reader understand applications of more complex methods. Evaluations are made to determine and predict efficiency and accuracy of presented models useful to wide a range of research areas along with many numerical examples for a deep understanding of the usefulness of each method. This book will make it possible for the researchers to tackle difficult problems and deepen their understanding of problem solving using numerical methods. Multipoint methods are of great practical importance, as they determine sequences of successive approximations for evaluative purposes. This is especially helpful in achieving the highest computational efficiency. The rapid development of digital computers and advanced computer arithmetic have provided a need for new methods useful to solving practical problems in a multitude of disciplines such as applied mathematics, computer science, engineering, physics, financial mathematics, and biology. - Provides a succinct way of implementing a wide range of useful and important numerical algorithms for solving research problems - Illustrates how numerical methods can be used to study problems which have applications in engineering and sciences, including signal processing, and control theory, and financial computation - Facilitates a deeper insight into the development of methods, numerical analysis of convergence rate, and very detailed analysis of computational efficiency - Provides a powerful means of learning by systematic experimentation with some of the many fascinating problems in science - Includes highly efficient algorithms convenient for the implementation into the most common computer algebra systems such as Mathematica, MatLab, and Maple
Advances In Iterative Methods For Nonlinear Equations
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Author : Sergio Amat
language : en
Publisher: Springer
Release Date : 2016-09-27
Advances In Iterative Methods For Nonlinear Equations written by Sergio Amat and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-27 with Mathematics categories.
This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, and applications. Many problems are stated in the form of nonlinear equations, using mathematical modeling. In particular, a wide range of problems in Applied Mathematics and in Engineering can be solved by finding the solutions to these equations. The book reveals the importance of studying convergence aspects in iterative methods and shows that selection of the most efficient and robust iterative method for a given problem is crucial to guaranteeing a good approximation. A number of sample criteria for selecting the optimal method are presented, including those regarding the order of convergence, the computational cost, and the stability, including the dynamics. This book will appeal to researchers whose field of interest is related to nonlinear problems and equations, and their approximation.
Solving Nonlinear Equations With Newton S Method
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Author : C. T. Kelley
language : en
Publisher: SIAM
Release Date : 2003-01-01
Solving Nonlinear Equations With Newton S Method written by C. T. Kelley and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
This book on Newton's method is a user-oriented guide to algorithms and implementation. In just over 100 pages, it shows, via algorithms in pseudocode, in MATLAB, and with several examples, how one can choose an appropriate Newton-type method for a given problem, diagnose problems, and write an efficient solver or apply one written by others. It contains trouble-shooting guides to the major algorithms, their most common failure modes, and the likely causes of failure. It also includes many worked-out examples (available on the SIAM website) in pseudocode and a collection of MATLAB codes, allowing readers to experiment with the algorithms easily and implement them in other languages.
Methods For Solving Systems Of Nonlinear Equations
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Author : Werner C. Rheinboldt
language : en
Publisher: SIAM
Release Date : 1998-01-01
Methods For Solving Systems Of Nonlinear Equations written by Werner C. Rheinboldt and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.
This second edition provides much-needed updates to the original volume. Like the first edition, it emphasizes the ideas behind the algorithms as well as their theoretical foundations and properties, rather than focusing strictly on computational details; at the same time, this new version is now largely self-contained and includes essential proofs. Additions have been made to almost every chapter, including an introduction to the theory of inexact Newton methods, a basic theory of continuation methods in the setting of differentiable manifolds, and an expanded discussion of minimization methods. New information on parametrized equations and continuation incorporates research since the first edition.
New Developments Of Newton Type Iterations For Solving Nonlinear Problems
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Author : Tugal Zhanlav
language : en
Publisher: Springer Nature
Release Date : 2024-08-06
New Developments Of Newton Type Iterations For Solving Nonlinear Problems written by Tugal Zhanlav and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-06 with Mathematics categories.
This comprehensive book delves into the intricacies of Newton-type methods for nonlinear equations, offering insights into their convergence, accelerations, and extensions. Divided into three parts, the book explores higher-order iterations for nonlinear equations and their systems, and their applications in linear algebra and some nonlinear problems of theoretical physics. Emphasizing the pivotal role of iteration parameters in shaping convergence and expanding the domain, the authors draw from their extensive collaborative research to systematically compile and elucidate these findings. Catering to readers, graduate students, and researchers in applied mathematics, numerical analysis, and related disciplines, this book serves as a valuable resource, synthesizing decades of research to advance understanding and practical application in the field
Multi Grid Methods And Applications
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Author : Wolfgang Hackbusch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Multi Grid Methods And Applications written by Wolfgang Hackbusch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Multi-grid methods are the most efficient tools for solving elliptic boundary value problems. The reader finds here an elementary introduction to multi-grid algorithms as well as a comprehensive convergence analysis. One section describes special applications (convection-diffusion equations, singular perturbation problems, eigenvalue problems, etc.). The book also contains a complete presentation of the multi-grid method of the second kind, which has important applications to integral equations (e.g. the "panel method") and to numerous other problems. Readers with a practical interest in multi-grid methods will benefit from this book as well as readers with a more theoretical interest.
Numerical Methods For Engineers And Scientists Second Edition
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Author : Joe D. Hoffman
language : en
Publisher: CRC Press
Release Date : 2001-05-31
Numerical Methods For Engineers And Scientists Second Edition written by Joe D. Hoffman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-05-31 with Mathematics categories.
Emphasizing the finite difference approach for solving differential equations, the second edition of Numerical Methods for Engineers and Scientists presents a methodology for systematically constructing individual computer programs. Providing easy access to accurate solutions to complex scientific and engineering problems, each chapter begins with objectives, a discussion of a representative application, and an outline of special features, summing up with a list of tasks students should be able to complete after reading the chapter- perfect for use as a study guide or for review. The AIAA Journal calls the book "...a good, solid instructional text on the basic tools of numerical analysis."
Efficient Methods For Solving Equations And Variational Inequalities
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Author : Ioannis K. Argyros
language : en
Publisher: Polimetrica s.a.s.
Release Date : 2009
Efficient Methods For Solving Equations And Variational Inequalities written by Ioannis K. Argyros and has been published by Polimetrica s.a.s. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.