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A Contemporary Study Of Iterative Methods

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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

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 : 1498763626
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.

Iterative Methods and Their Dynamics with Applications

Iterative Methods and Their Dynamics with Applications Book
Author : Ioannis K. Argyros,Angel Alberto Magrenan
Publisher : CRC Press
Release : 2017-02-13
ISBN : 9781498763608
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.

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.

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.

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
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 revised and selected from the 150 submissions. They are organized in the topical secions on computing; soft computing; general computing; modelling.

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.

Iterative Methods for Approximate Solution of Inverse Problems

Iterative Methods for Approximate Solution of Inverse Problems Book
Author : A.B. Bakushinsky,M.Yu. Kokurin
Publisher : Springer Science & Business Media
Release : 2007-09-28
ISBN : 140203122X
Language : En, Es, Fr & De

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Book Description :

This volume presents a unified approach to constructing iterative methods for solving irregular operator equations and provides rigorous theoretical analysis for several classes of these methods. The analysis of methods includes convergence theorems as well as necessary and sufficient conditions for their convergence at a given rate. The principal groups of methods studied in the book are iterative processes based on the technique of universal linear approximations, stable gradient-type processes, and methods of stable continuous approximations. Compared to existing monographs and textbooks on ill-posed problems, the main distinguishing feature of the presented approach is that it doesn’t require any structural conditions on equations under consideration, except for standard smoothness conditions. This allows to obtain in a uniform style stable iterative methods applicable to wide classes of nonlinear inverse problems. Practical efficiency of suggested algorithms is illustrated in application to inverse problems of potential theory and acoustic scattering. The volume can be read by anyone with a basic knowledge of functional analysis. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems.

Computational Theory of Iterative Methods

Computational Theory of Iterative Methods Book
Author : Ioannis Argyros
Publisher : Elsevier
Release : 2007-09-04
ISBN : 9780080560700
Language : En, Es, Fr & De

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Book Description :

The book is designed for researchers, students and practitioners interested in using fast and efficient iterative methods to approximate solutions of nonlinear equations. The following four major problems are addressed. Problem 1: Show that the iterates are well defined. Problem 2: concerns the convergence of the sequences generated by a process and the question of whether the limit points are, in fact solutions of the equation. Problem 3: concerns the economy of the entire operations. Problem 4: concerns with how to best choose a method, algorithm or software program to solve a specific type of problem and its description of when a given algorithm succeeds or fails. The book contains applications in several areas of applied sciences including mathematical programming and mathematical economics. There is also a huge number of exercises complementing the theory. - Latest convergence results for the iterative methods - Iterative methods with the least computational cost - Iterative methods with the weakest convergence conditions - Open problems on iterative methods

Point Estimation of Root Finding Methods

Point Estimation of Root Finding Methods Book
Author : Miodrag Petkovic
Publisher : Springer
Release : 2008-05-29
ISBN : 3540778519
Language : En, Es, Fr & De

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Book Description :

The problem of solving nonlinear equations and systems of equations ranks among the most signi?cant in the theory and practice, not only of applied mathematicsbutalsoofmanybranchesofengineeringsciences,physics,c- puter science, astronomy, ?nance, and so on. A glance at the bibliography and the list of great mathematicians who have worked on this topic points to a high level of contemporary interest. Although the rapid development of digital computers led to the e?ective implementation of many numerical methods, in practical realization, it is necessary to solve various problems such as computational e?ciency based on the total central processor unit time, the construction of iterative methods which possess a fast convergence in the presence of multiplicity (or clusters) of a desired solution, the control of rounding errors, information about error bounds of obtained approximate solution, stating computationally veri?able initial conditions that ensure a safe convergence, etc. It is the solution of these challenging problems that was the principal motivation for the present study. In this book, we are mainly concerned with the statement and study of initial conditions that provide the guaranteed convergence of an iterative method for solving equations of the form f(z) = 0. The traditional approach to this problem is mainly based on asymptotic convergence analysis using some strong hypotheses on di?erentiability and derivative bounds in a rather wide domain.

Numerical Methods for Equations and its Applications

Numerical Methods for Equations and its Applications Book
Author : Ioannis K. Argyros,Yeol J. Cho,Saïd Hilout
Publisher : CRC Press
Release : 2012-06-05
ISBN : 1578087538
Language : En, Es, Fr & De

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Book Description :

This book introduces advanced numerical-functional analysis to beginning computer science researchers. The reader is assumed to have had basic courses in numerical analysis, computer programming, computational linear algebra, and an introduction to real, complex, and functional analysis. Although the book is of a theoretical nature, each chapter contains several new theoretical results and important applications in engineering, in dynamic economics systems, in input-output system, in the solution of nonlinear and linear differential equations, and optimization problem.

Numerical Methods for Partial Differential Equations

Numerical Methods for Partial Differential Equations Book
Author : Vitoriano Ruas
Publisher : John Wiley & Sons
Release : 2016-04-25
ISBN : 1119111374
Language : En, Es, Fr & De

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Book Description :

Numerical Methods for Partial Differential Equations: An Introduction Vitoriano Ruas, Sorbonne Universités, UPMC - Université Paris 6, France A comprehensive overview of techniques for the computational solution of PDE's Numerical Methods for Partial Differential Equations: An Introduction covers the three most popular methods for solving partial differential equations: the finite difference method, the finite element method and the finite volume method. The book combines clear descriptions of the three methods, their reliability, and practical implementation aspects. Justifications for why numerical methods for the main classes of PDE's work or not, or how well they work, are supplied and exemplified. Aimed primarily at students of Engineering, Mathematics, Computer Science, Physics and Chemistry among others this book offers a substantial insight into the principles numerical methods in this class of problems are based upon. The book can also be used as a reference for research work on numerical methods for PDE’s. Key features: A balanced emphasis is given to both practical considerations and a rigorous mathematical treatment The reliability analyses for the three methods are carried out in a unified framework and in a structured and visible manner, for the basic types of PDE's Special attention is given to low order methods, as practitioner's overwhelming default options for everyday use New techniques are employed to derive known results, thereby simplifying their proof Supplementary material is available from a companion website.

Numerical Methods in Economics

Numerical Methods in Economics Book
Author : Kenneth L. Judd
Publisher : MIT Press
Release : 1998-09-28
ISBN : 9780262100717
Language : En, Es, Fr & De

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Book Description :

To harness the full power of computer technology, economists need to use a broad range of mathematical techniques. In this book, Kenneth Judd presents techniques from the numerical analysis and applied mathematics literatures and shows how to use them in economic analyses. The book is divided into five parts. Part I provides a general introduction. Part II presents basics from numerical analysis on R^n, including linear equations, iterative methods, optimization, nonlinear equations, approximation methods, numerical integration and differentiation, and Monte Carlo methods. Part III covers methods for dynamic problems, including finite difference methods, projection methods, and numerical dynamic programming. Part IV covers perturbation and asymptotic solution methods. Finally, Part V covers applications to dynamic equilibrium analysis, including solution methods for perfect foresight models and rational expectation models. A website contains supplementary material including programs and answers to exercises.

Contemporary Issues in Behavioral Finance

Contemporary Issues in Behavioral Finance Book
Author : Simon Grima,Ercan Özen,Hakan Boz,Jonathan Spiteri,Eleftherios Thalassinos
Publisher : Emerald Group Publishing
Release : 2019-07-04
ISBN : 1787698815
Language : En, Es, Fr & De

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Book Description :

This special edition of Contemporary Studies in Economic and Financial Analysis offers seventeen chapters from invited participants in the International Applied Social Science Congress, held in Turkey between the 19th and 21st April 2018.

Iterative Methods for Nonlinear Optimization Problems

Iterative Methods for Nonlinear Optimization Problems Book
Author : Samuel L. S. Jacoby,Janusz S. Kowalik,J. T. Pizzo
Publisher : Prentice Hall
Release : 1972
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Iterative Methods for Nonlinear Optimization Problems book written by Samuel L. S. Jacoby,Janusz S. Kowalik,J. T. Pizzo, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Autoethnography and Heuristic Inquiry for Doctoral Level Researchers Emerging Research and Opportunities

Autoethnography and Heuristic Inquiry for Doctoral Level Researchers  Emerging Research and Opportunities Book
Author : Throne, Robin
Publisher : IGI Global
Release : 2019-05-10
ISBN : 1522593675
Language : En, Es, Fr & De

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Book Description :

Many resources exist to help new doctoral investigators to understand and engage with the tenets and philosophies that underpin doctoral-level research to allow for a sample of self-as-subject research. Every day, new forms of researcher-participant data collection and analysis protocols and contributions to the respective discipline in the use of these methods are designed by doctoral researchers and other scholars for heuristic inquiry and autoethnography. Autoethnography and Heuristic Inquiry for Doctoral-Level Researchers: Emerging Research and Opportunities is an essential research publication that explores the conventions of autoethnography or heuristic research within the specific context of doctoral-level research. In contrast to similar resources, this book presents various and unique systematic methods and procedures used within current research for data collection, analysis, interpretation and representations of data, and study contributions to illustrate the varied nuances and many choices doctoral-level researchers have when their research design is founded on the principles and tenets of autoethnography or heuristic inquiry. Thus, this book is ideal for doctoral research supervisors, doctoral students, independent researchers, and academicians.

Asset Intelligence through Integration and Interoperability and Contemporary Vibration Engineering Technologies

Asset Intelligence through Integration and Interoperability and Contemporary Vibration Engineering Technologies Book
Author : Joseph Mathew,C.W. Lim,Lin Ma,Don Sands,Michael E. Cholette,Pietro Borghesani
Publisher : Springer
Release : 2018-11-11
ISBN : 3319957112
Language : En, Es, Fr & De

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Book Description :

These proceedings include a collection of papers on a range of topics presented at the 12th World Congress on Engineering Asset Management (WCEAM) in Brisbane, 2 – 4 August 2017. Effective strategies are required for managing complex engineering assets such as built environments, infrastructure, plants, equipment, hardware systems and components. Following the release of the ISO 5500x set of standards in 2014, the 12th WCEAM addressed important issues covering all aspects of engineering asset management across various sectors including health. The topics discussed by the congress delegates are grouped into a number of tracks, including strategies for investment and divestment of assets, operations and maintenance of assets, assessment of assets’ health conditions, risk and vulnerability, technologies, and systems for management of assets, standards, education, training and certification.

Computational Methods in the Management of Hydro environmental Systems

Computational Methods in the Management of Hydro environmental Systems Book
Author : Vahid Nassehi,Diganta Bhusan Das
Publisher : IWA Publishing
Release : 2007
ISBN : 1843390450
Language : En, Es, Fr & De

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Book Description :

This book provides concise, up-to-date and easy-to-follow information on an increasingly important area of hydro-environmental analysis and management. It covers important aspects of both surface and subsurface water quality management, as they are inseparable components of aquifers and the flow in physical domains occur in combination with the other. However, the main emphasis of the book is on the practical development and application of computer based algorithms, via appropriate schemes, to realistic problems. Mathematical theories are not discussed as they can be found in many expert books. All sections of the book include detailed descriptions of practical examples. It also, uniquely, gives explanations regarding the formulation of practical management schedules and tools for hydro-environmental systems. There is a lack of books dealing with the practical aspects of the application of computer modelling techniques to complex hydrodynamical phenomena, and this book has been written for professionals and researchers, especially those who are not trained mathematicians who, nevertheless, need to make managerial decisions. Computational Methods in the Management of Hydro-Environmental Systems will be an invaluable source of information for post-graduate level researchers and decision-makers who need to apply numerical modelling techniques to investigate hydrodynamic phenomena and pollutants dispersion in natural aquatic systems. Professionals and engineers, who now need to gain insights about the working of computer techniques for choosing appropriate schemes and applying them to realistic problems, will also value this work. Masters' level and final-year graduate students are also expected to benefit from the book.

Efficient Methods for Solving Equations and Variational Inequalities

Efficient Methods for Solving Equations and Variational Inequalities Book
Author : Ioannis Konstantinos 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 Konstantinos Argyros,Saïd Hilout, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.