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Computational Theory Of Iterative Methods

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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

Aspects of the Computational Theory for Certain Iterative Methods

Aspects of the Computational Theory for Certain Iterative Methods Book
Author : Ioannis Konstantinos Argyros,Saïd Hilout
Publisher : Polimetrica s.a.s.
Release : 2009
ISBN : 8876991514
Language : En, Es, Fr & De

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Book Description :

Download Aspects of the Computational Theory for Certain Iterative Methods 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.

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.

Intelligent Numerical Methods II Applications to Multivariate Fractional Calculus

Intelligent Numerical Methods II  Applications to Multivariate Fractional Calculus Book
Author : George A. Anastassiou,Ioannis K. Argyros
Publisher : Springer
Release : 2016-04-27
ISBN : 3319336061
Language : En, Es, Fr & De

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Book Description :

In this short monograph Newton-like and other similar numerical methods with applications to solving multivariate equations are developed, which involve Caputo type fractional mixed partial derivatives and multivariate fractional Riemann-Liouville integral operators. These are studied for the first time in the literature. The chapters are self-contained and can be read independently. An extensive list of references is given per chapter. The book’s results are expected to find applications in many areas of applied mathematics, stochastics, computer science and engineering. As such this short monograph is suitable for researchers, graduate students, to be used in graduate classes and seminars of the above subjects, also to be in all science and engineering libraries.

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

Numerical Methods in Computational Electrodynamics

Numerical Methods in Computational Electrodynamics Book
Author : Ursula van Rienen
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 3642568025
Language : En, Es, Fr & De

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Book Description :

treated in more detail. They are just specimen of larger classes of schemes. Es sentially, we have to distinguish between semi-analytical methods, discretiza tion methods, and lumped circuit models. The semi-analytical methods and the discretization methods start directly from Maxwell's equations. Semi-analytical methods are concentrated on the analytical level: They use a computer only to evaluate expressions and to solve resulting linear algebraic problems. The best known semi-analytical methods are the mode matching method, which is described in subsection 2. 1, the method of integral equations, and the method of moments. In the method of integral equations, the given boundary value problem is transformed into an integral equation with the aid of a suitable Greens' function. In the method of moments, which includes the mode matching method as a special case, the solution function is represented by a linear combination of appropriately weighted basis func tions. The treatment of complex geometrical structures is very difficult for these methods or only possible after geometric simplifications: In the method of integral equations, the Greens function has to satisfy the boundary condi tions. In the mode matching method, it must be possible to decompose the domain into subdomains in which the problem can be solved analytically, thus allowing to find the basis functions. Nevertheless, there are some ap plications for which the semi-analytic methods are the best suited solution methods. For example, an application from accelerator physics used the mode matching technique (see subsection 5. 4).

Iterative Methods for Large Linear Systems

Iterative Methods for Large Linear Systems Book
Author : David R. Kincaid,Linda J. Hayes
Publisher : Academic Press
Release : 2014-05-10
ISBN : 1483260208
Language : En, Es, Fr & De

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Book Description :

Iterative Methods for Large Linear Systems contains a wide spectrum of research topics related to iterative methods, such as searching for optimum parameters, using hierarchical basis preconditioners, utilizing software as a research tool, and developing algorithms for vector and parallel computers. This book provides an overview of the use of iterative methods for solving sparse linear systems, identifying future research directions in the mainstream of modern scientific computing with an eye to contributions of the past, present, and future. Different iterative algorithms that include the successive overrelaxation (SOR) method, symmetric and unsymmetric SOR methods, local (ad-hoc) SOR scheme, and alternating direction implicit (ADI) method are also discussed. This text likewise covers the block iterative methods, asynchronous iterative procedures, multilevel methods, adaptive algorithms, and domain decomposition algorithms. This publication is a good source for mathematicians and computer scientists interested in iterative methods for large linear systems.

The Theory and Applications of Iteration Methods

The Theory and Applications of Iteration Methods Book
Author : Ioannis K. Argyros,Ferenc Szidarovszky
Publisher : CRC Press
Release : 2018-05-04
ISBN : 1351408976
Language : En, Es, Fr & De

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Book Description :

The Theory and Applications of Iteration Methods focuses on an abstract iteration scheme that consists of the recursive application of a point-to-set mapping. Each chapter presents new theoretical results and important applications in engineering, dynamic economic systems, and input-output systems. At the end of each chapter, case studies and numerical examples are presented from different fields of engineering and economics. Following an outline of general iteration schemes, the authors extend the discrete time-scale Liapunov theory to time-dependent, higher order, nonlinear difference equations. The monotone convergence to the solution is examined in and comparison theorems are proven . Results generalize well-known classical theorems, such as the contraction mapping principle, the lemma of Kantorovich, the famous Gronwall lemma, and the stability theorem of Uzawa. The book explores conditions for the convergence of special single- and two-step methods such as Newton's method, modified Newton's method, and Newton-like methods generated by point-to-point mappings in a Banach space setting. Conditions are examined for monotone convergence of Newton's methods and their variants. Students and professionals in engineering, the physical sciences, mathematics, and economics will benefit from the book's detailed examples, step-by-step explanations, and effective organization.

Computational Modelling of Concrete Structures

Computational Modelling of Concrete Structures Book
Author : Nenad Bicanic,René Borst,Herbert Mang,Gunther Meschke
Publisher : CRC Press
Release : 2010-02-24
ISBN : 1439859574
Language : En, Es, Fr & De

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Book Description :

Since 1984 the EURO-C conference series (Split 1984, Zell am See 1990, Innsbruck 1994, Badgastein 1998, St Johann im Pongau 2003, Mayrhofen 2006, Schladming 2010) has provided a forum for academic discussion of the latest theoretical, algorithmic and modelling developments associated with computational simulations of concrete and concrete structure

Computational Methods for Linear Integral Equations

Computational Methods for Linear Integral Equations Book
Author : Prem Kythe,Pratap Puri
Publisher : Springer Science & Business Media
Release : 2002-04-26
ISBN : 9780817641924
Language : En, Es, Fr & De

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Book Description :

This book presents numerical methods and computational aspects for linear integral equations. Such equations occur in various areas of applied mathematics, physics, and engineering. The material covered in this book, though not exhaustive, offers useful techniques for solving a variety of problems. Historical information cover ing the nineteenth and twentieth centuries is available in fragments in Kantorovich and Krylov (1958), Anselone (1964), Mikhlin (1967), Lonseth (1977), Atkinson (1976), Baker (1978), Kondo (1991), and Brunner (1997). Integral equations are encountered in a variety of applications in many fields including continuum mechanics, potential theory, geophysics, electricity and mag netism, kinetic theory of gases, hereditary phenomena in physics and biology, renewal theory, quantum mechanics, radiation, optimization, optimal control sys tems, communication theory, mathematical economics, population genetics, queue ing theory, and medicine. Most of the boundary value problems involving differ ential equations can be converted into problems in integral equations, but there are certain problems which can be formulated only in terms of integral equations. A computational approach to the solution of integral equations is, therefore, an essential branch of scientific inquiry.

Numerical Methods for Partial Differential Equations

Numerical Methods for Partial Differential Equations Book
Author : William F. Ames
Publisher : Academic Press
Release : 2014-06-28
ISBN : 0080571301
Language : En, Es, Fr & De

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Book Description :

This volume is designed as an introduction to the concepts of modern numerical analysis as they apply to partial differential equations. The book contains many practical problems and their solutions, but at the same time, strives to expose the pitfalls--such as overstability, consistency requirements, and the danger of extrapolation to nonlinear problems methods used on linear problems. Numerical Methods for Partial Differential Equations, Third Edition reflects the great accomplishments that have taken place in scientific computation in the fifteen years since the Second Edition was published. This new edition is a drastic revision of the previous one, with new material on boundary elements, spectral methods, the methods of lines, and invariant methods. At the same time, the new edition retains the self-contained nature of the older version, and shares the clarity of its exposition and the integrity of its presentation. Material on finite elements and finite differences have been merged, and now constitute equal partners Additional material has been added on boundary elements, spectral methods, the method of lines, and invariant methods References have been updated, and reflect the additional material Self-contained nature of the Second Edition has been maintained Very suitable for PDE courses

Meshfree Methods for Partial Differential Equations VI

Meshfree Methods for Partial Differential Equations VI Book
Author : Michael Griebel,Marc Alexander Schweitzer
Publisher : Springer Science & Business Media
Release : 2012-12-16
ISBN : 3642329799
Language : En, Es, Fr & De

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Book Description :

Meshfree methods are a modern alternative to classical mesh-based discretization techniques such as finite differences or finite element methods. Especially in a time-dependent setting or in the treatment of problems with strongly singular solutions their independence of a mesh makes these methods highly attractive. This volume collects selected papers presented at the Sixth International Workshop on Meshfree Methods held in Bonn, Germany in October 2011. They address various aspects of this very active research field and cover topics from applied mathematics, physics and engineering. ​

Domain Decomposition Methods in Science and Engineering XXI

Domain Decomposition Methods in Science and Engineering XXI Book
Author : Jocelyne Erhel,Martin J. Gander,Laurence Halpern,Géraldine Pichot,Taoufik Sassi,Olof Widlund
Publisher : Springer
Release : 2014-10-10
ISBN : 3319057898
Language : En, Es, Fr & De

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Book Description :

This volume contains a selection of papers presented at the 21st international conference on domain decomposition methods in science and engineering held in Rennes, France, June 25-29, 2012. Domain decomposition is an active and interdisciplinary research discipline, focusing on the development, analysis and implementation of numerical methods for massively parallel computers. Domain decomposition methods are among the most efficient solvers for large scale applications in science and engineering. They are based on a solid theoretical foundation and shown to be scalable for many important applications. Domain decomposition techniques can also naturally take into account multiscale phenomena. This book contains the most recent results in this important field of research, both mathematically and algorithmically and allows the reader to get an overview of this exciting branch of numerical analysis and scientific computing.

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 : 1466517115
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 co

Computational Methods for Geodynamics

Computational Methods for Geodynamics Book
Author : Alik Ismail-Zadeh,Paul Tackley
Publisher : Cambridge University Press
Release : 2010-07-22
ISBN : 1139489356
Language : En, Es, Fr & De

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Book Description :

Written as both a textbook and a handy reference, this text deliberately avoids complex mathematics assuming only basic familiarity with geodynamic theory and calculus. Here, the authors have brought together the key numerical techniques for geodynamic modeling, demonstrations of how to solve problems including lithospheric deformation, mantle convection and the geodynamo. Building from a discussion of the fundamental principles of mathematical and numerical modeling, the text moves into critical examinations of each of the different techniques before concluding with a detailed analysis of specific geodynamic applications. Key differences between methods and their respective limitations are also discussed - showing readers when and how to apply a particular method in order to produce the most accurate results. This is an essential text for advanced courses on numerical and computational modeling in geodynamics and geophysics, and an invaluable resource for researchers looking to master cutting-edge techniques. Links to supplementary computer codes are available online.

Fundamentals of Computation Theory

Fundamentals of Computation Theory Book
Author : R. V. Freĭvald
Publisher : Springer Science & Business Media
Release : 2001-08-03
ISBN : 3540424873
Language : En, Es, Fr & De

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Book Description :

This book constitutes the refereed proceedings of the 13th International Symposium Fundamentals of Computation Theory, FCT 2001, as well as of the International Workshop on Efficient Algorithms, WEA 2001, held in Riga, Latvia, in August 2001. The 28 revised full FCT papers and 15 short papers presented together with six invited contributions and 8 revised full WEA papers as well as three invited WEA contributions have been carefully reviewed and selected. Among the topics addressed are a broad variety of topics from theoretical computer science, algorithmics and programming theory. The WEA papers deal with graph and network algorithms, flow and routing problems, scheduling and approximation algorithms, etc.

Fundamentals of Computation Theory

Fundamentals of Computation Theory Book
Author : Lothar Budach,Rais G. Bukharajev,Oleg Borisovič Lupanov,Oleg B. Lupanov
Publisher : Springer Science & Business Media
Release : 1987-12-09
ISBN : 9783540187400
Language : En, Es, Fr & De

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Book Description :

This volume contains abridged versions of most of the sectional talks and some invited lectures given at the International Conference on Fundamentals of Computation Theory held at Kazan State University, Kazan, USSR, June 22-26, 1987. The conference was the sixth in the series of FCT Conferences organized every odd year, and the first one to take place in the USSR. FCT '87 was organized by the Section of Discrete Mathematics of the Academy of Sciences in the USSR, the Moscow State University (Department of Discrete Mathematics), and the Kazan State University (Department of Theoretical Cybernetics). This volume contains selected contributions to the following fields: Mathematical Models of Computation, Synthesis and Complexity of Control Systems, Probabilistic Computations, Theory of Programming, Computer-Assisted Deduction. The volume reflects the fact that FCT '87 was organized in the USSR: A wide range of problems typical of research in Mathematical Cybernetics in the USSR is comprehensively represented.

Optimization with PDE Constraints

Optimization with PDE Constraints Book
Author : Ronald Hoppe
Publisher : Springer
Release : 2014-09-11
ISBN : 3319080253
Language : En, Es, Fr & De

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Book Description :

This book on PDE Constrained Optimization contains contributions on the mathematical analysis and numerical solution of constrained optimal control and optimization problems where a partial differential equation (PDE) or a system of PDEs appears as an essential part of the constraints. The appropriate treatment of such problems requires a fundamental understanding of the subtle interplay between optimization in function spaces and numerical discretization techniques and relies on advanced methodologies from the theory of PDEs and numerical analysis as well as scientific computing. The contributions reflect the work of the European Science Foundation Networking Programme ’Optimization with PDEs’ (OPTPDE).

Recent Advances in Algorithmic Differentiation

Recent Advances in Algorithmic Differentiation Book
Author : Shaun Forth,Paul Hovland,Eric Phipps,Jean Utke,Andrea Walther
Publisher : Springer Science & Business Media
Release : 2012-07-30
ISBN : 3642300235
Language : En, Es, Fr & De

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Book Description :

The proceedings represent the state of knowledge in the area of algorithmic differentiation (AD). The 31 contributed papers presented at the AD2012 conference cover the application of AD to many areas in science and engineering as well as aspects of AD theory and its implementation in tools. For all papers the referees, selected from the program committee and the greater community, as well as the editors have emphasized accessibility of the presented ideas also to non-AD experts. In the AD tools arena new implementations are introduced covering, for example, Java and graphical modeling environments or join the set of existing tools for Fortran. New developments in AD algorithms target the efficiency of matrix-operation derivatives, detection and exploitation of sparsity, partial separability, the treatment of nonsmooth functions, and other high-level mathematical aspects of the numerical computations to be differentiated. Applications stem from the Earth sciences, nuclear engineering, fluid dynamics, and chemistry, to name just a few. In many cases the applications in a given area of science or engineering share characteristics that require specific approaches to enable AD capabilities or provide an opportunity for efficiency gains in the derivative computation. The description of these characteristics and of the techniques for successfully using AD should make the proceedings a valuable source of information for users of AD tools.

Coping with Complexity Model Reduction and Data Analysis

Coping with Complexity  Model Reduction and Data Analysis Book
Author : Alexander N. Gorban,Dirk Roose
Publisher : Springer Science & Business Media
Release : 2010-10-21
ISBN : 9783642149412
Language : En, Es, Fr & De

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Book Description :

This volume contains the extended version of selected talks given at the international research workshop "Coping with Complexity: Model Reduction and Data Analysis", Ambleside, UK, August 31 – September 4, 2009. The book is deliberately broad in scope and aims at promoting new ideas and methodological perspectives. The topics of the chapters range from theoretical analysis of complex and multiscale mathematical models to applications in e.g., fluid dynamics and chemical kinetics.