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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

A Contemporary Study of Iterative Methods

A Contemporary Study of Iterative Methods Book
Author : A. Alberto Magrenan,Ioannis Argyros
Publisher : Academic Press
Release : 2018-02-16
ISBN : 9780128092149
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 : 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.

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.

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.

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.

Advanced Numerical Methods for Differential Equations

Advanced Numerical Methods for Differential Equations Book
Author : Harendra Singh,Jagdev Singh,Sunil Dutt Purohit,Devendra Kumar
Publisher : CRC Press
Release : 2021-07-29
ISBN : 1000381080
Language : En, Es, Fr & De

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Book Description :

Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models. This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and science. Engineers, mathematicians, scientists, and researchers working on real-life mathematical problems will find this book useful.

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.

Optimized Iterative Methods with Applications in Diverse Disciplines

Optimized Iterative Methods with Applications in Diverse Disciplines Book
Author : Samundra Regmi
Publisher : Nova Science Publishers
Release : 2021-04-21
ISBN : 9781536195088
Language : En, Es, Fr & De

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Book Description :

"Numerous problems from diverse disciplines can be converted using mathematical modeling to an equation defined on suitable abstract spaces usually involving the n-dimensional Euclidean space, Hilbert space, Banach Space or even more general spaces. The solution of these equations is sought in closed form. But this is possible only in special cases. That is why researchers and practitioners use iterative algorithms, which seem to be the only alternative. Due to the explosion of technology, faster and faster computers become available. This development simply means that new optimized algorithms should be developed to take advantage of these improvements. That is exactly where we come in with our book containing such algorithms with applications in problems from numerical analysis and economics but also from other areas such as biology, chemistry, physics, parallel computing, and engineering. The book is an outgrowth of scientific research conducted over two years. This book can be used by senior undergraduate students, graduate students, researchers, and practitioners in the aforementioned areas in the classroom or as reference material. Readers should know the fundamentals of numerical-functional analysis, economic theory, and Newtonian physics. Some knowledge of computers and contemporary programming shall be very helpful to readers"--

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.

Newton Methods

Newton Methods Book
Author : Ioannis K. Argyros
Publisher : Nova Publishers
Release : 2005
ISBN : 9781594540523
Language : En, Es, Fr & De

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Book Description :

This self-contained treatment offers a contemporary and systematic development of the theory and application of Newton methods, which are undoubtedly the most effective tools for solving equations appearing in computational sciences. Its focal point resides in an exhaustive analysis of the convergence properties of several Newton variants used in connection to specific real life problems originated from astrophysics, engineering, mathematical economics and other applied areas. What distinguishes this book from others is the fact that the weak convergence conditions inaugurated here allow for a wider applicability of Newton methods; finer error bounds on the distances involved, and a more precise information on the location of the solution. These factors make this book ideal for researchers, practitioners and students.

Classical and Modern Numerical Analysis

Classical and Modern Numerical Analysis Book
Author : Azmy S. Ackleh,Edward James Allen,R. Baker Kearfott,Padmanabhan Seshaiyer
Publisher : CRC Press
Release : 2009-07-20
ISBN : 1420091581
Language : En, Es, Fr & De

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Book Description :

Classical and Modern Numerical Analysis: Theory, Methods and Practice provides a sound foundation in numerical analysis for more specialized topics, such as finite element theory, advanced numerical linear algebra, and optimization. It prepares graduate students for taking doctoral examinations in numerical analysis.The text covers the main areas o

Applied Iterative Methods

Applied Iterative Methods Book
Author : CHARLES L. BYRNE
Publisher : A K PETERS
Release : 2021-09-30
ISBN : 9780367446161
Language : En, Es, Fr & De

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Book Description :

This book is a collection of essays on iterative algorithms and their uses. It focuses on the mathematics of medical image reconstruction, with emphasis on Fourier inversion. The book discusses the problems and algorithms in the context of operators on finite-dimensional Euclidean space.

A First Course in Numerical Methods

A First Course in Numerical Methods Book
Author : Uri M. Ascher,Chen Greif
Publisher : SIAM
Release : 2011-07-14
ISBN : 0898719976
Language : En, Es, Fr & De

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Book Description :

Offers students a practical knowledge of modern techniques in scientific computing.

Materials for Modern Technologies VI

Materials for Modern Technologies VI Book
Author : Sergei Alexandrov,Bingang Xu
Publisher : Trans Tech Publications Ltd
Release : 2020-07-20
ISBN : 3035736855
Language : En, Es, Fr & De

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Book Description :

Selected peer-reviewed full text papers from Spring International Conference on Material Sciences and Technology (MST-S 2020) Selected, peer-reviewed papers from the 2020 Spring International Conference on Material Sciences and Technology (MST-S), August 14-16, 2020, Kunming, China

Iterative Methods in Combinatorial Optimization

Iterative Methods in Combinatorial Optimization Book
Author : Lap Chi Lau,R. Ravi,Mohit Singh
Publisher : Cambridge University Press
Release : 2011-04-18
ISBN : 1139499394
Language : En, Es, Fr & De

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Book Description :

With the advent of approximation algorithms for NP-hard combinatorial optimization problems, several techniques from exact optimization such as the primal-dual method have proven their staying power and versatility. This book describes a simple and powerful method that is iterative in essence and similarly useful in a variety of settings for exact and approximate optimization. The authors highlight the commonality and uses of this method to prove a variety of classical polyhedral results on matchings, trees, matroids and flows. The presentation style is elementary enough to be accessible to anyone with exposure to basic linear algebra and graph theory, making the book suitable for introductory courses in combinatorial optimization at the upper undergraduate and beginning graduate levels. Discussions of advanced applications illustrate their potential for future application in research in approximation algorithms.

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.

Modern Techniques in Computational Chemistry MOTECCTM 90

Modern Techniques in Computational Chemistry  MOTECCTM 90 Book
Author : E. Clementi
Publisher : Springer
Release : 1990-08-31
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Modern Techniques in Computational Chemistry MOTECCTM 90 book written by E. Clementi, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.