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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 K. 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 K. 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 : 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.

Numerical Computations Theory and Algorithms

Numerical Computations  Theory and Algorithms Book
Author : Yaroslav D. Sergeyev,Dmitri E. Kvasov
Publisher : Springer Nature
Release : 2020-02-13
ISBN : 3030390810
Language : En, Es, Fr & De

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Book Description :

The two-volume set LNCS 11973 and 11974 constitute revised selected papers from the Third International Conference on Numerical Computations: Theory and Algorithms, NUMTA 2019, held in Crotone, Italy, in June 2019. This volume, LNCS 11973, consists of 34 full and 18 short papers chosen among papers presented at special streams and sessions of the Conference. The papers in part I were organized following the topics of these special sessions: approximation: methods, algorithms, and applications; computational methods for data analysis; first order methods in optimization: theory and applications; high performance computing in modelling and simulation; numbers, algorithms, and applications; optimization and management of water supply.

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

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.

Functional Numerical Methods Applications to Abstract Fractional Calculus

Functional Numerical Methods  Applications to Abstract Fractional Calculus Book
Author : George A. Anastassiou,Ioannis K. Argyros
Publisher : Springer
Release : 2017-10-27
ISBN : 3319695266
Language : En, Es, Fr & De

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Book Description :

This book presents applications of Newton-like and other similar methods to solve abstract functional equations involving fractional derivatives. It focuses on Banach space-valued functions of a real domain – studied for the first time in the literature. Various issues related to the modeling and analysis of fractional order systems continue to grow in popularity, and the book provides a deeper and more formal analysis of selected issues that are relevant to many areas – including decision-making, complex processes, systems modeling and control – and deeply embedded in the fields of engineering, computer science, physics, economics, and the social and life sciences. The book offers a valuable resource for researchers and graduate students, and can also be used as a textbook for seminars on the above-mentioned subjects. All chapters are self-contained and can be read independently. Further, each chapter includes an extensive list of references.

Computational Methods for Numerical Analysis with R

Computational Methods for Numerical Analysis with R Book
Author : James P Howard, II
Publisher : CRC Press
Release : 2017-07-12
ISBN : 1498723640
Language : En, Es, Fr & De

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Book Description :

Computational Methods for Numerical Analysis with R is an overview of traditional numerical analysis topics presented using R. This guide shows how common functions from linear algebra, interpolation, numerical integration, optimization, and differential equations can be implemented in pure R code. Every algorithm described is given with a complete function implementation in R, along with examples to demonstrate the function and its use. Computational Methods for Numerical Analysis with R is intended for those who already know R, but are interested in learning more about how the underlying algorithms work. As such, it is suitable for statisticians, economists, and engineers, and others with a computational and numerical background.

Iterative Methods and Preconditioners for Systems of Linear Equations

Iterative Methods and Preconditioners for Systems of Linear Equations Book
Author : Gabriele Ciaramella,Martin J. Gander
Publisher : SIAM
Release : 2022-02-08
ISBN : 1611976901
Language : En, Es, Fr & De

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Book Description :

Iterative methods use successive approximations to obtain more accurate solutions. This book gives an introduction to iterative methods and preconditioning for solving discretized elliptic partial differential equations and optimal control problems governed by the Laplace equation, for which the use of matrix-free procedures is crucial. All methods are explained and analyzed starting from the historical ideas of the inventors, which are often quoted from their seminal works. Iterative Methods and Preconditioners for Systems of Linear Equations grew out of a set of lecture notes that were improved and enriched over time, resulting in a clear focus for the teaching methodology, which derives complete convergence estimates for all methods, illustrates and provides MATLAB codes for all methods, and studies and tests all preconditioners first as stationary iterative solvers. This textbook is appropriate for undergraduate and graduate students who want an overview or deeper understanding of iterative methods. Its focus on both analysis and numerical experiments allows the material to be taught with very little preparation, since all the arguments are self-contained, and makes it appropriate for self-study as well. It can be used in courses on iterative methods, Krylov methods and preconditioners, and numerical optimal control. Scientists and engineers interested in new topics and applications will also find the text useful.

Boundary and Interior Layers Computational and Asymptotic Methods BAIL 2014

Boundary and Interior Layers  Computational and Asymptotic Methods   BAIL 2014 Book
Author : Petr Knobloch
Publisher : Springer
Release : 2016-04-19
ISBN : 3319257277
Language : En, Es, Fr & De

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Book Description :

This volume offers contributions reflecting a selection of the lectures presented at the international conference BAIL 2014, which was held from 15th to 19th September 2014 at the Charles University in Prague, Czech Republic. These are devoted to the theoretical and/or numerical analysis of problems involving boundary and interior layers and methods for solving these problems numerically. The authors are both mathematicians (pure and applied) and engineers, and bring together a large number of interesting ideas. The wide variety of topics treated in the contributions provides an excellent overview of current research into the theory and numerical solution of problems involving boundary and interior layers.

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.

Numerical Methods in Computational Mechanics

Numerical Methods in Computational Mechanics Book
Author : Jamshid Ghaboussi,Xiping Steven Wu
Publisher : CRC Press
Release : 2016-11-25
ISBN : 1315351641
Language : En, Es, Fr & De

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Book Description :

This book explores the numerical algorithms underpinning modern finite element based computational mechanics software. It covers all the major numerical methods that are used in computational mechanics. It reviews the basic concepts in linear algebra and advanced matrix theory, before covering solution of systems of equations, symmetric eigenvalue solution methods, and direct integration of discrete dynamic equations of motion, illustrated with numerical examples. This book suits a graduate course in mechanics based disciplines, and will help software developers in computational mechanics. Increased understanding of the underlying numerical methods will also help practicing engineers to use the computational mechanics software more effectively.

Programming for Computations MATLAB Octave

Programming for Computations   MATLAB Octave Book
Author : Svein Linge,Hans Petter Langtangen
Publisher : Springer
Release : 2016-08-01
ISBN : 3319324527
Language : En, Es, Fr & De

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Book Description :

This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.

Computational Methods in Power System Analysis

Computational Methods in Power System Analysis Book
Author : Reijer Idema,Domenico J.P. Lahaye
Publisher : Springer
Release : 2014-07-08
ISBN : 9462390649
Language : En, Es, Fr & De

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Book Description :

This book treats state-of-the-art computational methods for power flow studies and contingency analysis. In the first part the authors present the relevant computational methods and mathematical concepts. In the second part, power flow and contingency analysis are treated. Furthermore, traditional methods to solve such problems are compared to modern solvers, developed using the knowledge of the first part of the book. Finally, these solvers are analyzed both theoretically and experimentally, clearly showing the benefits of the modern approach.

Numerical Methods of Mathematical Optimization

Numerical Methods of Mathematical Optimization Book
Author : Hans P. Künzi,H. G. Tzschach,C. A. Zehnder
Publisher : Academic Press
Release : 2014-05-12
ISBN : 1483264718
Language : En, Es, Fr & De

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Book Description :

Numerical Methods of Mathematical Optimization: With ALGOL and FORTRAN Programs reviews the theory and the practical application of the numerical methods of mathematical optimization. An ALGOL and a FORTRAN program was developed for each one of the algorithms described in the theoretical section. This should result in easy access to the application of the different optimization methods. Comprised of four chapters, this volume begins with a discussion on the theory of linear and nonlinear optimization, with the main stress on an easily understood, mathematically precise presentation. In addition to the theoretical considerations, several algorithms of importance to the numerical application of optimization theory are described. The next chapter explains the computer programs used in actual optimization, which have the form of procedures or subroutines. The book concludes with an analysis of ALGOL and FORTRAN, paying particular attention to their use in global optimization procedures as well as for the simplex and duoplex methods and the decomposition, Gomory, Beale, and Wolfe algorithms. This monograph will be helpful to students and practitioners of computer science and applied mathematics.

Numerical Methods in Matrix Computations

Numerical Methods in Matrix Computations Book
Author : Åke Björck
Publisher : Springer
Release : 2014-10-07
ISBN : 3319050893
Language : En, Es, Fr & De

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Book Description :

Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work.

Krylov Methods for Nonsymmetric Linear Systems

Krylov Methods for Nonsymmetric Linear Systems Book
Author : Gérard Meurant,Jurjen Duintjer Tebbens
Publisher : Springer Nature
Release : 2020-10-02
ISBN : 3030552519
Language : En, Es, Fr & De

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Book Description :

This book aims to give an encyclopedic overview of the state-of-the-art of Krylov subspace iterative methods for solving nonsymmetric systems of algebraic linear equations and to study their mathematical properties. Solving systems of algebraic linear equations is among the most frequent problems in scientific computing; it is used in many disciplines such as physics, engineering, chemistry, biology, and several others. Krylov methods have progressively emerged as the iterative methods with the highest efficiency while being very robust for solving large linear systems; they may be expected to remain so, independent of progress in modern computer-related fields such as parallel and high performance computing. The mathematical properties of the methods are described and analyzed along with their behavior in finite precision arithmetic. A number of numerical examples demonstrate the properties and the behavior of the described methods. Also considered are the methods’ implementations and coding as Matlab®-like functions. Methods which became popular recently are considered in the general framework of Q-OR (quasi-orthogonal )/Q-MR (quasi-minimum) residual methods. This book can be useful for both practitioners and for readers who are more interested in theory. Together with a review of the state-of-the-art, it presents a number of recent theoretical results of the authors, some of them unpublished, as well as a few original algorithms. Some of the derived formulas might be useful for the design of possible new methods or for future analysis. For the more applied user, the book gives an up-to-date overview of the majority of the available Krylov methods for nonsymmetric linear systems, including well-known convergence properties and, as we said above, template codes that can serve as the base for more individualized and elaborate implementations.

Numerical Techniques for Global Atmospheric Models

Numerical Techniques for Global Atmospheric Models Book
Author : Peter H. Lauritzen,Christiane Jablonowski,Mark A. Taylor,Ramachandran D. Nair
Publisher : Springer Science & Business Media
Release : 2011-03-29
ISBN : 364211640X
Language : En, Es, Fr & De

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Book Description :

This book surveys recent developments in numerical techniques for global atmospheric models. It is based upon a collection of lectures prepared by leading experts in the field. The chapters reveal the multitude of steps that determine the global atmospheric model design. They encompass the choice of the equation set, computational grids on the sphere, horizontal and vertical discretizations, time integration methods, filtering and diffusion mechanisms, conservation properties, tracer transport, and considerations for designing models for massively parallel computers. A reader interested in applied numerical methods but also the many facets of atmospheric modeling should find this book of particular relevance.

Finite Difference Computing with PDEs

Finite Difference Computing with PDEs Book
Author : Hans Petter Langtangen,Svein Linge
Publisher : Springer
Release : 2017-06-21
ISBN : 3319554565
Language : En, Es, Fr & De

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Book Description :

This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.

Numerical Mathematics and Advanced Applications ENUMATH 2017

Numerical Mathematics and Advanced Applications ENUMATH 2017 Book
Author : Florin Adrian Radu,Kundan Kumar,Inga Berre,Jan Martin Nordbotten,Iuliu Sorin Pop
Publisher : Springer
Release : 2019-01-05
ISBN : 3319964151
Language : En, Es, Fr & De

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Book Description :

This book collects many of the presented papers, as plenary presentations, mini-symposia invited presentations, or contributed talks, from the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) 2017. The conference was organized by the University of Bergen, Norway from September 25 to 29, 2017. Leading experts in the field presented the latest results and ideas in the designing, implementation, and analysis of numerical algorithms as well as their applications to relevant, societal problems. ENUMATH is a series of conferences held every two years to provide a forum for discussing basic aspects and new trends in numerical mathematics and scientific and industrial applications. These discussions are upheld at the highest level of international expertise. The first ENUMATH conference was held in Paris in 1995 with successive conferences being held at various locations across Europe, including Heidelberg (1997), Jyvaskyla (1999), lschia Porto (2001), Prague (2003), Santiago de Compostela (2005), Graz (2007), Uppsala (2009), Leicester (2011), Lausanne (2013), and Ankara (2015).