Computational Theory of Iterative Methods

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

Produk Detail:

• Author : Ioannis Argyros
• Publisher : Elsevier
• Pages : 504 pages
• ISBN : 9780080560700
• Rating : 5/5 from 1 reviews

Computational Theory of Iterative Methods

• Author : Ioannis Argyros
• Publisher : Elsevier
• Release : 04 September 2007

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

A Contemporary Study of Iterative Methods

• Author : A. Alberto Magrenan,Ioannis Argyros
• Release : 13 February 2018

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

Iterative Methods and Their Dynamics with Applications

• Author : Ioannis Konstantinos Argyros,Angel Alberto Magreñán
• Publisher : CRC Press
• Release : 12 July 2017

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

Functional Numerical Methods: Applications to Abstract Fractional Calculus

• Author : George A. Anastassiou,Ioannis K. Argyros
• Publisher : Springer
• Release : 27 October 2017

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 –

Handbook of Optimization

• Author : Ivan Zelinka,Václav Snásel,Ajith Abraham
• Publisher : Springer Science & Business Media
• Release : 13 August 2012

Optimization problems were and still are the focus of mathematics from antiquity to the present. Since the beginning of our civilization, the human race has had to confront numerous technological challenges, such as finding the optimal solution of various problems including control technologies, power sources construction, applications in economy, mechanical engineering and energy distribution amongst others. These examples encompass both ancient as well as modern technologies like the first electrical energy distribution network in USA etc. Some of the key

Computational Methods in Nonlinear Analysis

• Author : Ioannis K. Argyros,Sad Hilout
• Publisher : World Scientific
• Release : 24 May 2022

The field of computational sciences has seen a considerable development in mathematics, engineering sciences, and economic equilibrium theory. Researchers in this field are faced with the problem of solving a variety of equations or variational inequalities. We note that in computational sciences, the practice of numerical analysis for finding such solutions is essentially connected to variants of Newton's method. The efficient computational methods for finding the solutions of fixed point problems, nonlinear equations and variational inclusions are the first goal

Applications of MATLAB in Science and Engineering

• Publisher : BoD – Books on Demand
• Release : 09 September 2011

The book consists of 24 chapters illustrating a wide range of areas where MATLAB tools are applied. These areas include mathematics, physics, chemistry and chemical engineering, mechanical engineering, biological (molecular biology) and medical sciences, communication and control systems, digital signal, image and video processing, system modeling and simulation. Many interesting problems have been included throughout the book, and its contents will be beneficial for students and professionals in wide areas of interest.

Proceedings of the international conference "“NUMERICAL COMPUTATIONS: THEORY AND ALGORITHMS”

• Author : Yaroslav D. Sergeyev,Dmitri E. Kvasov,Francesco Dell'Accio
• Publisher : Luigi Pellegrini Editore
• Release : 27 June 2013

This book contains Proceedings of the International Conference and Summer School NUMTA-2013 “Numerical Computations: Theory and Algorithms”. The Conference is organized jointly by the University of Calabria, Italy, and by the N.I. Lobachevsky State University of Nizhni Novgorod, Russia in cooperation with the Society for Industrial and Applied Mathematics (SIAM), USA. The goal of the Conference is to create a multidisciplinary round table for an open discussion on numerical modeling nature by using traditional and emerging computational paradigms. The

Templates for the Solution of Linear Systems

• Author : Richard Barrett,Michael W. Berry,Tony F. Chan,James Demmel,June Donato,Jack Dongarra,Victor Eijkhout,Roldan Pozo,Charles Romine,Henk van der Vorst
• Publisher : SIAM
• Release : 01 January 1994

In this book, which focuses on the use of iterative methods for solving large sparse systems of linear equations, templates are introduced to meet the needs of both the traditional user and the high-performance specialist. Templates, a description of a general algorithm rather than the executable object or source code more commonly found in a conventional software library, offer whatever degree of customization the user may desire. Templates offer three distinct advantages: they are general and reusable; they are not

Numerical Methods of Mathematical Optimization

• Author : Hans P. Künzi,H. G. Tzschach,C. A. Zehnder
• Release : 12 May 2014

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

A Survey of Preconditioned Iterative Methods

• Author : Are Magnus Bruaset
• Publisher : Routledge
• Release : 13 December 2018

The problem of solving large, sparse, linear systems of algebraic equations is vital in scientific computing, even for applications originating from quite different fields. A Survey of Preconditioned Iterative Methods presents an up to date overview of iterative methods for numerical solution of such systems. Typically, the methods considered are w

Proceedings of the 4th International Conference on Frontiers in Intelligent Computing: Theory and Applications (FICTA) 2015

• Author : Swagatam Das,Tandra Pal,Samarjit Kar,Suresh Chandra Satapathy,Jyotsna Kumar Mandal
• Publisher : Springer
• Release : 24 October 2015

The proceedings of the 4th International Conference on Frontiers in Intelligent Computing: Theory and Applications 2015 (FICTA 2015) serves as the knowledge centre not only for scientists and researchers in the field of intelligent computing but also for students of post-graduate level in various engineering disciplines. The book covers a comprehensive overview of the theory, methods, applications and tools of Intelligent Computing. Researchers are now working in interdisciplinary areas and the proceedings of FICTA 2015 plays a major role to accumulate those significant

Iterative Methods for Linear Systems

• Author : Maxim A. Olshanskii,Eugene E. Tyrtyshnikov
• Publisher : SIAM
• Release : 21 July 2014

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.÷÷