Computational Theory of Iterative Methods Book
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Computational Theory of Iterative Methods


  • Author : Ioannis Argyros
  • Publisher : Elsevier
  • Release Date : 2007-09-04
  • Genre: Mathematics
  • Pages : 504
  • ISBN 10 : 0080560709

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Computational Theory of Iterative Methods 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

A Contemporary Study of Iterative Methods Book

A Contemporary Study of Iterative Methods


  • Author : A. Alberto Magrenan
  • Publisher : Academic Press
  • Release Date : 2018-02-13
  • Genre: Mathematics
  • Pages : 400
  • ISBN 10 : 9780128094938

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A Contemporary Study of Iterative Methods 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 Book

Iterative Methods and Their Dynamics with Applications


  • Author : Ioannis Konstantinos Argyros
  • Publisher : CRC Press
  • Release Date : 2017-07-12
  • Genre: Mathematics
  • Pages : 365
  • ISBN 10 : 9781351649506

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Iterative Methods and Their Dynamics with Applications 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 Book

Intelligent Numerical Methods II Applications to Multivariate Fractional Calculus


  • Author : George A. Anastassiou
  • Publisher : Springer
  • Release Date : 2016-04-27
  • Genre: Computers
  • Pages : 116
  • ISBN 10 : 9783319336060

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Intelligent Numerical Methods II Applications to Multivariate Fractional Calculus 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.

Iterative Methods for Linear Systems Book

Iterative Methods for Linear Systems


  • Author : Maxim A. Olshanskii
  • Publisher : SIAM
  • Release Date : 2014-07-21
  • Genre: Mathematics
  • Pages : 244
  • ISBN 10 : 9781611973464

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Iterative Methods for Linear Systems Book Description :

Iterative Methods for Linear Systems÷offers a mathematically rigorous introduction to fundamental iterative methods for systems of linear algebraic equations. The book distinguishes itself from other texts on the topic by providing a straightforward yet comprehensive analysis of the Krylov subspace methods, approaching the development and analysis of algorithms from various algorithmic and mathematical perspectives, and going beyond the standard description of iterative methods by connecting them in a natural way to the idea of preconditioning.÷÷

Computational Methods for Linear Integral Equations Book

Computational Methods for Linear Integral Equations


  • Author : Prem Kythe
  • Publisher : Springer Science & Business Media
  • Release Date : 2002-04-26
  • Genre: Mathematics
  • Pages : 508
  • ISBN 10 : 0817641920

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Computational Methods for Linear Integral Equations 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.

Classical and Modern Numerical Analysis Book

Classical and Modern Numerical Analysis


  • Author : Azmy S. Ackleh
  • Publisher : CRC Press
  • Release Date : 2009-07-20
  • Genre: Mathematics
  • Pages : 628
  • ISBN 10 : 1420091581

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Classical and Modern Numerical Analysis 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 of introductory numerical analysis, including the solution of nonlinear equations, numerical linear algebra, ordinary differential equations, approximation theory, numerical integration, and boundary value problems. Focusing on interval computing in numerical analysis, it explains interval arithmetic, interval computation, and interval algorithms. The authors illustrate the concepts with many examples as well as analytical and computational exercises at the end of each chapter. This advanced, graduate-level introduction to the theory and methods of numerical analysis supplies the necessary background in numerical methods so that students can apply the techniques and understand the mathematical literature in this area. Although the book is independent of a specific computer program, MATLAB® code is available on the authors' website to illustrate various concepts.

Numerical Methods in Computational Electrodynamics Book

Numerical Methods in Computational Electrodynamics


  • Author : Ursula van Rienen
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • Genre: Computers
  • Pages : 375
  • ISBN 10 : 9783642568022

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Numerical Methods in Computational Electrodynamics 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).

The Theory and Applications of Iteration Methods Book

The Theory and Applications of Iteration Methods


  • Author : Ioannis K. Argyros
  • Publisher : CRC Press
  • Release Date : 2018-05-04
  • Genre: Science
  • Pages : 368
  • ISBN 10 : 9781351408974

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The Theory and Applications of Iteration Methods 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.

Iterative Algorithms Book

Iterative Algorithms


  • Author : Ioannis K. Argyros
  • Publisher : Nova Science Publishers
  • Release Date : 2016-09-01
  • Genre: Algorithms
  • Pages : 490
  • ISBN 10 : 1634854063

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Iterative Algorithms Book Description :

It is a well-known fact that iterative methods have been studied concerning problems where mathematicians cannot find a solution in a closed form. There exist methods with different behaviors when they are applied to different functions and methods with higher order of convergence, methods with great zones of convergence, methods which do not require the evaluation of any derivative, and optimal methods among others. It should come as no surprise, therefore, that researchers are developing new iterative methods frequently. Once these iterative methods appear, several researchers study them in different terms: convergence conditions, real dynamics, complex dynamics, optimal order of convergence, etc. These phenomena motivated the authors to study the most used and classical ones, for example Newton's method, Halleys method and/or its derivative-free alternatives. Related to the convergence of iterative methods, the most well-known conditions are the ones created by Kantorovich, who developed a theory which has allowed many researchers to continue and experiment with these conditions. Many authors in recent years have studied modifications of these conditions related, for example, to centered conditions, omega-conditions and even convergence in Hilbert spaces. In this monograph, the authors present their complete work done in the past decade in analysing convergence and dynamics of iterative methods. It is the natural outgrowth of their related publications in these areas. Chapters are self-contained and can be read independently. Moreover, an extensive list of references is given in each chapter in order to allow the reader to use the previous ideas. For these reasons, the authors think that several advanced courses can be taught using this book. The book's results are expected to help find applications in many areas of applied mathematics, engineering, computer science and real problems. As such, this monograph is suitable to researchers, graduate students and semin

Iterative Methods for Toeplitz Systems Book

Iterative Methods for Toeplitz Systems


  • Author : Michael K. Ng
  • Publisher : Numerical Mathematics and Scie
  • Release Date : 2004
  • Genre: Mathematics
  • Pages : 350
  • ISBN 10 : 0198504209

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Iterative Methods for Toeplitz Systems Book Description :

Toeplitz and Toeplitz-related systems arise in a variety of applications in mathematics and engineering, especially in signal and image processing. This book deals primarily with iterative methods for solving Toeplitz and Toeplitz-related linear systems, discussing both the algorithms and their convergence theories. A basic knowledge of real analysis, elementary numerical analysis and linear algebra is assumed. The first part of the book (chapters one and two) gives a brief review of some terms and results in linear algebra and the conjugate gradient method, which are important topics for handling the mathematics later on in the book. The second part of the book (chapters three to seven) presents the theory of using iterative methods for solving Toeplitz and Toeplitz-related systems. The third part of the book (chapters eight to twelve) presents recent results from applying the use of iterative methods in different fields of applications, such as partial differential equations, signal and image processing, integral equations and queuing networks. These chapters provide research and application-oriented readers with a thorough understanding of using iterative methods, enabling them not only to apply these methods to the problems discussed but also to derive and analyze new methods for other types of problems and applications.

Iterative Methods for Large Linear Systems Book

Iterative Methods for Large Linear Systems


  • Author : David R. Kincaid
  • Publisher : Academic Press
  • Release Date : 2014-05-10
  • Genre: Mathematics
  • Pages : 350
  • ISBN 10 : 9781483260204

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Iterative Methods for Large Linear Systems 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.

Computational Modelling of Concrete Structures Book

Computational Modelling of Concrete Structures


  • Author : Nenad Bicanic
  • Publisher : CRC Press
  • Release Date : 2010-02-24
  • Genre: Technology & Engineering
  • Pages : 836
  • ISBN 10 : 9781439859575

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Computational Modelling of Concrete Structures 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

Numerical Methods in Finance Book
Score: 5
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Numerical Methods in Finance


  • Author : Paolo Brandimarte
  • Publisher : John Wiley & Sons
  • Release Date : 2003-10-13
  • Genre: Mathematics
  • Pages : 432
  • ISBN 10 : 9780471461692

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Numerical Methods in Finance Book Description :

Balanced coverage of the methodology and theory of numericalmethods in finance Numerical Methods in Finance bridges the gap between financialtheory and computational practice while helping students andpractitioners exploit MATLAB for financial applications. Paolo Brandimarte covers the basics of finance and numericalanalysis and provides background material that suits the needs ofstudents from both financial engineering and economicsperspectives. Classical numerical analysis methods; optimization,including less familiar topics such as stochastic and integerprogramming; simulation, including low discrepancy sequences; andpartial differential equations are covered in detail. Extensiveillustrative examples of the application of all of thesemethodologies are also provided. The text is primarily focused on MATLAB-based application, but alsoincludes descriptions of other readily available toolboxes that arerelevant to finance. Helpful appendices on the basics of MATLAB andprobability theory round out this balanced coverage. Accessible forstudents-yet still a useful reference for practitioners-NumericalMethods in Finance offers an expert introduction to powerful toolsin finance.

Iterative Krylov Methods for Large Linear Systems Book
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Iterative Krylov Methods for Large Linear Systems


  • Author : H. A. van der Vorst
  • Publisher : Cambridge University Press
  • Release Date : 2003-04-17
  • Genre: Mathematics
  • Pages : 221
  • ISBN 10 : 0521818281

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Iterative Krylov Methods for Large Linear Systems Book Description :

Overview of iterative solutions methods for systems of linear equations. For graduate students and researchers.

Functions of Matrices Book

Functions of Matrices


  • Author : Nicholas J. Higham
  • Publisher : SIAM
  • Release Date : 2008
  • Genre: Factorization (Mathematics)
  • Pages : 425
  • ISBN 10 : 9780898717778

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Functions of Matrices Book Description :

A thorough and elegant treatment of the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms. Key features include a detailed treatment of the matrix sign function and matrix roots; a development of the theory of conditioning and properties of the Fre;chet derivative; Schur decomposition; block Parlett recurrence; a thorough analysis of the accuracy, stability, and computational cost of numerical methods; general results on convergence and stability of matrix iterations; and a chapter devoted to the f(A)b problem. Ideal for advanced courses and for self-study, its broad content, references and appendix also make this book a convenient general reference. Contains an extensive collection of problems with solutions and MATLAB implementations of key algorithms.

Iterative Methods in Scientific Computing and Their Applications Book

Iterative Methods in Scientific Computing and Their Applications


  • Author : Raymond Chan
  • Publisher : Springer
  • Release Date : 1997-04
  • Genre: Computers
  • Pages : 384
  • ISBN 10 : UVA:X004190824

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Iterative Methods in Scientific Computing and Their Applications Book Description :

Because of the rapid evolution of the development of this field, as well as the fact that iterative methods are not often developed in a generic form for general applications, there is a lack of published materials that treat the topic properly and fully. These lectures from the Winter School on Iterative Methods in Scientific Computing and their Applications aims to bridge such a gap in the literature.