# Computational Theory Of Iterative Methods

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## Computational Theory of Iterative Methods

Author | : Ioannis Argyros |

Publsiher | : Elsevier |

Total Pages | : 504 |

Release | : 2007-09-04 |

ISBN | : 9780080560700 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Computational Theory of Iterative Methods Book Excerpt:**

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

Author | : Ioannis K. Argyros,Saïd Hilout |

Publsiher | : Polimetrica s.a.s. |

Total Pages | : 581 |

Release | : 2009 |

ISBN | : 8876991514 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Aspects of the Computational Theory for Certain Iterative Methods Book Excerpt:**

## The Theory and Applications of Iteration Methods

Author | : Ioannis K. Argyros |

Publsiher | : CRC Press |

Total Pages | : 470 |

Release | : 2022-01-21 |

ISBN | : 1000536750 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**The Theory and Applications of Iteration Methods Book Excerpt:**

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.

## Iterative Methods and Their Dynamics with Applications

Author | : Ioannis Konstantinos Argyros,Angel Alberto Magreñán |

Publsiher | : CRC Press |

Total Pages | : 365 |

Release | : 2017-07-12 |

ISBN | : 1498763626 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Iterative Methods and Their Dynamics with Applications Book Excerpt:**

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

Author | : Yaroslav D. Sergeyev,Dmitri E. Kvasov |

Publsiher | : Springer Nature |

Total Pages | : 622 |

Release | : 2020-02-13 |

ISBN | : 3030390810 |

Category | : Computers |

Language | : EN, FR, DE, ES & NL |

**Numerical Computations Theory and Algorithms Book Excerpt:**

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

Author | : A. Alberto Magrenan,Ioannis Argyros |

Publsiher | : Academic Press |

Total Pages | : 400 |

Release | : 2018-02-13 |

ISBN | : 0128094931 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**A Contemporary Study of Iterative Methods Book Excerpt:**

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

## Intelligent Numerical Methods II Applications to Multivariate Fractional Calculus

Author | : George A. Anastassiou,Ioannis K. Argyros |

Publsiher | : Springer |

Total Pages | : 116 |

Release | : 2016-04-27 |

ISBN | : 3319336061 |

Category | : Technology & Engineering |

Language | : EN, FR, DE, ES & NL |

**Intelligent Numerical Methods II Applications to Multivariate Fractional Calculus Book Excerpt:**

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.

## Numerical Methods for Equations and its Applications

Author | : Ioannis K. Argyros,Yeol J. Cho,Saïd Hilout |

Publsiher | : CRC Press |

Total Pages | : 474 |

Release | : 2012-06-05 |

ISBN | : 1466517115 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Numerical Methods for Equations and its Applications Book Excerpt:**

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

## Intelligent Numerical Methods Applications to Fractional Calculus

Author | : George A. Anastassiou,Ioannis K. Argyros |

Publsiher | : Springer |

Total Pages | : 423 |

Release | : 2015-12-07 |

ISBN | : 3319267213 |

Category | : Technology & Engineering |

Language | : EN, FR, DE, ES & NL |

**Intelligent Numerical Methods Applications to Fractional Calculus Book Excerpt:**

In this monograph the authors present Newton-type, Newton-like and other numerical methods, which involve fractional derivatives and fractional integral operators, for the first time studied in the literature. All for the purpose to solve numerically equations whose associated functions can be also non-differentiable in the ordinary sense. That is among others extending the classical Newton method theory which requires usual differentiability of function. Chapters are self-contained and can be read independently and several advanced courses can be taught out of this book. 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 monograph is suitable for researchers, graduate students, and seminars of the above subjects, also to be in all science and engineering libraries.

## Numerical Methods in Computational Electrodynamics

Author | : Ursula van Rienen |

Publsiher | : Springer Science & Business Media |

Total Pages | : 375 |

Release | : 2012-12-06 |

ISBN | : 3642568025 |

Category | : Computers |

Language | : EN, FR, DE, ES & NL |

**Numerical Methods in Computational Electrodynamics Book Excerpt:**

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).

## Functional Numerical Methods Applications to Abstract Fractional Calculus

Author | : George A. Anastassiou,Ioannis K. Argyros |

Publsiher | : Springer |

Total Pages | : 161 |

Release | : 2017-10-27 |

ISBN | : 3319695266 |

Category | : Technology & Engineering |

Language | : EN, FR, DE, ES & NL |

**Functional Numerical Methods Applications to Abstract Fractional Calculus Book Excerpt:**

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.

## Optimization and Dynamics with Their Applications

Author | : Akio Matsumoto |

Publsiher | : Springer |

Total Pages | : 344 |

Release | : 2017-05-23 |

ISBN | : 9811042144 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Optimization and Dynamics with Their Applications Book Excerpt:**

This book presents a variety of advanced research papers in optimization and dynamics written by internationally recognized researchers in these fields. As an example of applying optimization in sport, it introduces a new method for finding the optimal bat sizes in baseball and softball. The book is divided into three parts: operations research, dynamics, and applications. The operations research section deals with the convergence of Newton-type iterations for solving nonlinear equations and optimum problems, the limiting properties of the Nash bargaining solution, the utilization of public goods, and optimizing lot sizes in the automobile industry. The topics in dynamics include special linear approximations of nonlinear systems, the dynamic behavior of industrial clusters, adaptive learning in oligopolies, periodicity in duopolies resulting from production constraints, and dynamic models of love affairs. The third part presents applications in the fields of reverse logistic network design for end-of-life wind turbines, fuzzy optimization of the structure of agricultural products, water resources management in the restoration plans for a lake and also in groundwater supplies. In addition it discusses applications in reliability engineering to find the optimal preventive replacement times of deteriorating equipment and using bargaining theory to determine the best maintenance contract. The diversity of the application areas clearly illustrates the usefulness of the theory and methodology of optimization and dynamics in solving practical problems.

## Numerical Methods for Large Eigenvalue Problems

Author | : Yousef Saad |

Publsiher | : SIAM |

Total Pages | : 292 |

Release | : 2011-01-01 |

ISBN | : 9781611970739 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Numerical Methods for Large Eigenvalue Problems Book Excerpt:**

This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.

## Numerical Methods in Economics

Author | : Kenneth L. Judd |

Publsiher | : MIT Press |

Total Pages | : 662 |

Release | : 1998-09-28 |

ISBN | : 9780262100717 |

Category | : Business & Economics |

Language | : EN, FR, DE, ES & NL |

**Numerical Methods in Economics Book Excerpt:**

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

## Computational Methods for Numerical Analysis with R

Author | : James P Howard, II |

Publsiher | : CRC Press |

Total Pages | : 257 |

Release | : 2017-07-12 |

ISBN | : 1498723640 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Computational Methods for Numerical Analysis with R Book Excerpt:**

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.

## Numerical Methods in Computational Finance

Author | : Daniel J. Duffy |

Publsiher | : John Wiley & Sons |

Total Pages | : 544 |

Release | : 2022-03-14 |

ISBN | : 1119719720 |

Category | : Business & Economics |

Language | : EN, FR, DE, ES & NL |

**Numerical Methods in Computational Finance Book Excerpt:**

This book is a detailed and step-by-step introduction to the mathematical foundations of ordinary and partial differential equations, their approximation by the finite difference method and applications to computational finance. The book is structured so that it can be read by beginners, novices and expert users. Part A Mathematical Foundation for One-Factor Problems Chapters 1 to 7 introduce the mathematical and numerical analysis concepts that are needed to understand the finite difference method and its application to computational finance. Part B Mathematical Foundation for Two-Factor Problems Chapters 8 to 13 discuss a number of rigorous mathematical techniques relating to elliptic and parabolic partial differential equations in two space variables. In particular, we develop strategies to preprocess and modify a PDE before we approximate it by the finite difference method, thus avoiding ad-hoc and heuristic tricks. Part C The Foundations of the Finite Difference Method (FDM) Chapters 14 to 17 introduce the mathematical background to the finite difference method for initial boundary value problems for parabolic PDEs. It encapsulates all the background information to construct stable and accurate finite difference schemes. Part D Advanced Finite Difference Schemes for Two-Factor Problems Chapters 18 to 22 introduce a number of modern finite difference methods to approximate the solution of two factor partial differential equations. This is the only book we know of that discusses these methods in any detail. Part E Test Cases in Computational Finance Chapters 23 to 26 are concerned with applications based on previous chapters. We discuss finite difference schemes for a wide range of one-factor and two-factor problems. This book is suitable as an entry-level introduction as well as a detailed treatment of modern methods as used by industry quants and MSc/MFE students in finance. The topics have applications to numerical analysis, science and engineering. More on computational finance and the author’s online courses, see www.datasim.nl.

## Iterative Methods and Preconditioners for Systems of Linear Equations

Author | : Gabriele Ciaramella,Martin J. Gander |

Publsiher | : SIAM |

Total Pages | : 285 |

Release | : 2022-02-08 |

ISBN | : 1611976901 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Iterative Methods and Preconditioners for Systems of Linear Equations Book Excerpt:**

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.

## Numerical Methods in Matrix Computations

Author | : Åke Björck |

Publsiher | : Springer |

Total Pages | : 800 |

Release | : 2014-10-07 |

ISBN | : 3319050893 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Numerical Methods in Matrix Computations Book Excerpt:**

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.

## Computational Sciences Modelling Computing and Soft Computing

Author | : Ashish Awasthi,Sunil Jacob John,Satyananda Panda |

Publsiher | : Springer Nature |

Total Pages | : 271 |

Release | : 2021-07-27 |

ISBN | : 9811647720 |

Category | : Computers |

Language | : EN, FR, DE, ES & NL |

**Computational Sciences Modelling Computing and Soft Computing Book Excerpt:**

This book constitutes revised and selected papers of the First International Conference on Computational Sciences - Modelling, Computing and Soft Computing, held in Kozhikode, Kerala, India, in September 2020. The 15 full papers and 6 short papers presented were thoroughly reviewed and selected from the 150 submissions. They are organized in the topical secions on computing; soft computing; general computing; modelling.

## Iterative Methods for Large Linear Systems

Author | : David R. Kincaid,Linda J. Hayes |

Publsiher | : Academic Press |

Total Pages | : 350 |

Release | : 2014-05-10 |

ISBN | : 1483260208 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Iterative Methods for Large Linear Systems Book Excerpt:**

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.