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Multipoint Methods For Solving Nonlinear Equations

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Multipoint Methods for Solving Nonlinear Equations

Multipoint Methods for Solving Nonlinear Equations Book
Author : Miodrag Petkovic,Beny Neta,Ljiljana Petkovic,Jovana Dzunic
Publisher : Academic Press
Release : 2012-12-31
ISBN : 0123972981
Language : En, Es, Fr & De

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Book Description :

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

Iterative Methods for Solving Nonlinear Equations and Systems

Iterative Methods for Solving Nonlinear Equations and Systems Book
Author : Juan R. Torregrosa,Alicia Cordero,Fazlollah Soleymani
Publisher : MDPI
Release : 2019-12-06
ISBN : 3039219405
Language : En, Es, Fr & De

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Book Description :

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.

Advances in Iterative Methods for Nonlinear Equations

Advances in Iterative Methods for Nonlinear Equations Book
Author : Sergio Amat,Sonia Busquier
Publisher : Springer
Release : 2016-09-27
ISBN : 331939228X
Language : En, Es, Fr & De

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Book Description :

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.

Computational Science and its Applications

Computational Science and its Applications Book
Author : A. H. Siddiqi,R. C. Singh,G. D. Veerappa Gowda
Publisher : CRC Press
Release : 2020-10-21
ISBN : 1000193691
Language : En, Es, Fr & De

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Book Description :

Computational science is a rapidly growing multidisciplinary field concerned with the design, implementation, and use of mathematical models to analyze and solve real-world problems. It is an area of science that spans many disciplines and which involves the development of models and allows the use of computers to perform simulations or numerical analysis to understand problems that are computational and theoretical. Computational Science and its Applications provides an opportunity for readers to develop abilities to pose and solve problems that combine insights from one or more disciplines from the natural sciences with mathematical tools and computational skills. This requires a unique combination of applied and theoretical knowledge and skills. The topics covered in this edited book are applications of wavelet and fractals, modeling by partial differential equations on flat structure as well as on graphs and networks, computational linguistics, prediction of natural calamities and diseases like epilepsy seizure, heart attack, stroke, biometrics, modeling through inverse problems, interdisciplinary topics of physics, mathematics, and medical science, and modeling of terrorist attacks and human behavior. The focus of this book is not to educate computer specialists, but to provide readers with a solid understanding of basic science as well as an integrated knowledge on how to use essential methods from computational science. Features: Modeling of complex systems Cognitive computing systems for real-world problems Presentation of inverse problems in medical science and their numerical solutions Challenging research problems in many areas of computational science This book could be used as a reference book for researchers working in theoretical research as well as those who are doing modeling and simulation in such disciplines as physics, biology, geoscience, and mathematics, and those who have a background in computational science.

Multipoint Methods for Solving Nonlinear Equations

Multipoint Methods for Solving Nonlinear Equations Book
Author : Miodrag Petković,Beny Neta,Ljiljana Petkovic,Jovana Dzunic
Publisher : Unknown
Release : 2013
ISBN : 9780123970138
Language : En, Es, Fr & De

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Book Description :

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

Symmetry with Operator Theory and Equations

Symmetry with Operator Theory and Equations Book
Author : Ioannis Argyros
Publisher : MDPI
Release : 2019-10-21
ISBN : 303921666X
Language : En, Es, Fr & De

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Book Description :

A plethora of problems from diverse disciplines such as Mathematics, Mathematical: Biology, Chemistry, Economics, Physics, Scientific Computing and also Engineering can be formulated as an equation defined in abstract spaces using Mathematical Modelling. The solutions of these equations can be found in closed form only in special case. That is why researchers and practitioners utilize iterative procedures from which a sequence is being generated approximating the solution under some conditions on the initial data. This type of research is considered most interesting and challenging. This is our motivation for the introduction of this special issue on Iterative Procedures.

The Theory and Applications of Iteration Methods

The Theory and Applications of Iteration Methods Book
Author : Ioannis K. Argyros
Publisher : CRC Press
Release : 2022-01-21
ISBN : 1000536777
Language : En, Es, Fr & De

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Book Description :

The theory and applications of Iteration Methods is a very fast-developing field of numerical analysis and computer methods. The second edition is completely updated and continues to present the state-of-the-art contemporary theory of iteration methods with practical applications, exercises, case studies, and examples of where and how they can be used. The Theory and Applications of Iteration Methods, Second Edition includes newly developed iteration methods taking advantage of the most recent technology (computers, robots, machines). It extends the applicability of well-established methods by increasing the convergence domain and offers sharper error tolerance. New proofs and ideas for handling convergence are introduced along with a new variety of story problems picked from diverse disciplines. This new edition is for researchers, practitioners, and students in engineering, economics, and computational sciences.

Numerical Methods for Energy Applications

Numerical Methods for Energy Applications Book
Author : Naser Mahdavi Tabatabaei,Nicu Bizon
Publisher : Springer Nature
Release : 2021-07-03
ISBN : 303062191X
Language : En, Es, Fr & De

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Book Description :

This book provides a thorough guide to the use of numerical methods in energy systems and applications. It presents methods for analysing engineering applications for energy systems, discussing finite difference, finite element, and other advanced numerical methods. Solutions to technical problems relating the application of these methods to energy systems are also thoroughly explored. Readers will discover diverse perspectives of the contributing authors and extensive discussions of issues including: • a wide variety of numerical methods concepts and related energy systems applications;• systems equations and optimization, partial differential equations, and finite difference method;• methods for solving nonlinear equations, special methods, and their mathematical implementation in multi-energy sources;• numerical investigations of electrochemical fields and devices; and• issues related to numerical approaches and optimal integration of energy consumption. This is a highly informative and carefully presented book, providing scientific and academic insight for readers with an interest in numerical methods and energy systems.

Iterative Methods and Their Dynamics with Applications

Iterative Methods and Their Dynamics with Applications Book
Author : Ioannis Konstantinos Argyros,Angel Alberto Magreñán
Publisher : CRC Press
Release : 2017-07-12
ISBN : 1351649507
Language : En, Es, Fr & De

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Book Description :

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.

Mathematical Analysis and Computing

Mathematical Analysis and Computing Book
Author : R. N. Mohapatra,S. Yugesh,G. Kalpana,C. Kalaivani
Publisher : Springer Nature
Release : 2021-05-05
ISBN : 9813346469
Language : En, Es, Fr & De

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Book Description :

This book is a collection of selected papers presented at the International Conference on Mathematical Analysis and Computing (ICMAC 2019) held at Sri Sivasubramaniya Nadar College of Engineering, Chennai, India, from 23–24 December 2019. Having found its applications in game theory, economics, and operations research, mathematical analysis plays an important role in analyzing models of physical systems and provides a sound logical base for problems stated in a qualitative manner. This book aims at disseminating recent advances in areas of mathematical analysis, soft computing, approximation and optimization through original research articles and expository survey papers. This book will be of value to research scholars, professors, and industrialists working in these areas.

Computational Sciences Modelling Computing and Soft Computing

Computational Sciences   Modelling  Computing and Soft Computing Book
Author : Ashish Awasthi,Sunil Jacob John,Satyananda Panda
Publisher : Springer Nature
Release : 2021-07-27
ISBN : 9811647720
Language : En, Es, Fr & De

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Book Description :

This book constitutes revised and selected papers of the First International Conference on Computational Sciences - Modelling, Computing and Soft Computing, held in Kozhikode, Kerala, India, in September 2020. The 15 full papers and 6 short papers presented were thoroughly reviewed and selected from the 150 submissions. They are organized in the topical secions on computing; soft computing; general computing; modelling.

Numerical Methods for Roots of Polynomials

Numerical Methods for Roots of Polynomials   Book
Author : J.M. McNamee,Victor Pan
Publisher : Newnes
Release : 2013-07-19
ISBN : 008093143X
Language : En, Es, Fr & De

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Book Description :

Numerical Methods for Roots of Polynomials - Part II along with Part I (9780444527295) covers most of the traditional methods for polynomial root-finding such as interpolation and methods due to Graeffe, Laguerre, and Jenkins and Traub. It includes many other methods and topics as well and has a chapter devoted to certain modern virtually optimal methods. Additionally, there are pointers to robust and efficient programs. This book is invaluable to anyone doing research in polynomial roots, or teaching a graduate course on that topic. First comprehensive treatment of Root-Finding in several decades with a description of high-grade software and where it can be downloaded Offers a long chapter on matrix methods and includes Parallel methods and errors where appropriate Proves invaluable for research or graduate course

Efficient Methods for Solving Equations and Variational Inequalities

Efficient Methods for Solving Equations and Variational Inequalities Book
Author : Ioannis K. Argyros,Saïd Hilout
Publisher : Polimetrica s.a.s.
Release : 2009
ISBN : 8876991492
Language : En, Es, Fr & De

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Book Description :

Download Efficient Methods for Solving Equations and Variational Inequalities book written by Ioannis K. Argyros,Saïd Hilout, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Mathematical Analysis and its Applications

Mathematical Analysis and its Applications Book
Author : P. N. Agrawal,R. N. Mohapatra,Uaday Singh,H. M. Srivastava
Publisher : Springer
Release : 2015-08-22
ISBN : 813222485X
Language : En, Es, Fr & De

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Book Description :

This book discusses recent developments in and the latest research on mathematics, statistics and their applications. All contributing authors are eminent academics, scientists, researchers and scholars in their respective fields, hailing from around the world. The book presents roughly 60 unpublished, high-quality and peer-reviewed research papers that cover a broad range of areas including approximation theory, harmonic analysis, operator theory, fixed-point theory, functional differential equations, dynamical and control systems, complex analysis, special functions, function spaces, summability theory, Fourier and wavelet analysis, and numerical analysis – all of which are topics of great interest to the research community – while further papers highlight important applications of mathematical analysis in science, engineering and related areas. This conference aims at bringing together experts and young researchers in mathematics from all over the world to discuss the latest advances in mathematical analysis and at promoting the exchange of ideas in various applications of mathematics in engineering, physics and biology. This conference encourages international collaboration and provides young researchers an opportunity to learn about the current state of the research in their respective fields.

Symmetry in Applied Mathematics

Symmetry in Applied Mathematics Book
Author : Lorentz Jäntschi,Sorana D. Bolboacă
Publisher : MDPI
Release : 2021-01-26
ISBN : 3039437917
Language : En, Es, Fr & De

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Book Description :

Applied mathematics and symmetry work together as a powerful tool for problem reduction and solving. We are communicating applications in probability theory and statistics (A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested, The Asymmetric Alpha-Power Skew-t Distribution), fractals - geometry and alike (Khovanov Homology of Three-Strand Braid Links, Volume Preserving Maps Between p-Balls, Generation of Julia and Mandelbrot Sets via Fixed Points), supersymmetry - physics, nanostructures -chemistry, taxonomy - biology and alike (A Continuous Coordinate System for the Plane by Triangular Symmetry, One-Dimensional Optimal System for 2D Rotating Ideal Gas, Minimal Energy Configurations of Finite Molecular Arrays, Noether-Like Operators and First Integrals for Generalized Systems of Lane-Emden Equations), algorithms, programs and software analysis (Algorithm for Neutrosophic Soft Sets in Stochastic Multi-Criteria Group Decision Making Based on Prospect Theory, On a Reduced Cost Higher Order Traub-Steffensen-Like Method for Nonlinear Systems, On a Class of Optimal Fourth Order Multiple Root Solvers without Using Derivatives) to specific subjects (Facility Location Problem Approach for Distributed Drones, Parametric Jensen-Shannon Statistical Complexity and Its Applications on Full-Scale Compartment Fire Data). Diverse topics are thus combined to map out the mathematical core of practical problems.

A Contemporary Study of Iterative Methods

A Contemporary Study of Iterative Methods Book
Author : A. Alberto Magrenan,Ioannis Argyros
Publisher : Academic Press
Release : 2018-02-13
ISBN : 0128094931
Language : En, Es, Fr & De

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Book Description :

A Contemporary Study of Iterative Methods: Convergence, Dynamics and Applications evaluates and compares advances in iterative techniques, also discussing their numerous applications in applied mathematics, engineering, mathematical economics, mathematical biology and other applied sciences. It uses the popular iteration technique in generating the approximate solutions of complex nonlinear equations that is suitable for aiding in the solution of advanced problems in engineering, mathematical economics, mathematical biology and other applied sciences. Iteration methods are also applied for solving optimization problems. In such cases, the iteration sequences converge to an optimal solution of the problem at hand. Contains recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces Encompasses the novel tool of dynamic analysis for iterative methods, including new developments in Smale stability theory and polynomiography Explores the uses of computation of iterative methods across non-linear analysis Uniquely places discussion of derivative-free methods in context of other discoveries, aiding comparison and contrast between options

Finite Difference Methods Theory and Applications

Finite Difference Methods  Theory and Applications Book
Author : Ivan Dimov,István Faragó,Lubin Vulkov
Publisher : Springer
Release : 2019-01-28
ISBN : 3030115399
Language : En, Es, Fr & De

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Book Description :

This book constitutes the refereed conference proceedings of the 7th International Conference on Finite Difference Methods, FDM 2018, held in Lozenetz, Bulgaria, in June 2018.The 69 revised full papers presented together with 11 invited papers were carefully reviewed and selected from 94 submissions. They deal with many modern and new numerical techniques like splitting techniques, Green’s function method, multigrid methods, and immersed interface method.

Zeroing Neural Networks

Zeroing Neural Networks Book
Author : Lin Xiao,Lei Jia
Publisher : John Wiley & Sons
Release : 2022-11-09
ISBN : 1119986036
Language : En, Es, Fr & De

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Book Description :

Zeroing Neural Networks Describes the theoretical and practical aspects of finite-time ZNN methods for solving an array of computational problems Zeroing Neural Networks (ZNN) have become essential tools for solving discretized sensor-driven time-varying matrix problems in engineering, control theory, and on-chip applications for robots. Building on the original ZNN model, finite-time zeroing neural networks (FTZNN) enable efficient, accurate, and predictive real-time computations. Setting up discretized FTZNN algorithms for different time-varying matrix problems requires distinct steps. Zeroing Neural Networks provides in-depth information on the finite-time convergence of ZNN models in solving computational problems. Divided into eight parts, this comprehensive resource covers modeling methods, theoretical analysis, computer simulations, nonlinear activation functions, and more. Each part focuses on a specific type of time-varying computational problem, such as the application of FTZNN to the Lyapunov equation, linear matrix equation, and matrix inversion. Throughout the book, tables explain the performance of different models, while numerous illustrative examples clarify the advantages of each FTZNN method. In addition, the book: Describes how to design, analyze, and apply FTZNN models for solving computational problems Presents multiple FTZNN models for solving time-varying computational problems Details the noise-tolerance of FTZNN models to maximize the adaptability of FTZNN models to complex environments Includes an introduction, problem description, design scheme, theoretical analysis, illustrative verification, application, and summary in every chapter Zeroing Neural Networks: Finite-time Convergence Design, Analysis and Applications is an essential resource for scientists, researchers, academic lecturers, and postgraduates in the field, as well as a valuable reference for engineers and other practitioners working in neurocomputing and intelligent control.

Iterative Methods for the Solution of Equations

Iterative Methods for the Solution of Equations Book
Author : Joseph Frederick Traub
Publisher : Unknown
Release : 1964
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Iterative Methods for the Solution of Equations book written by Joseph Frederick Traub, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

New Trends in Applied Analysis and Computational Mathematics

New Trends in Applied Analysis and Computational Mathematics Book
Author : Susanta Kumar Paikray,Hemen Dutta,John N. Mordeson
Publisher : Springer Nature
Release : 2021-06-28
ISBN : 9811614024
Language : En, Es, Fr & De

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Book Description :

The volume contains original research papers as the Proceedings of the International Conference on Advances in Mathematics and Computing, held at Veer Surendra Sai University of Technology, Odisha, India, on 7-8 February, 2020. It focuses on new trends in applied analysis, computational mathematics and related areas. It also includes certain new models, image analysis technique, fluid flow problems, etc. as applications of mathematical analysis and computational mathematics. The volume should bring forward new and emerging topics of mathematics and computing having potential applications and uses in other areas of sciences. It can serve as a valuable resource for graduate students, researchers and educators interested in mathematical tools and techniques for solving various problems arising in science and engineering.