Computational Theory of Iterative Methods

Computational Theory of Iterative Methods
Author: Ioannis Argyros
Publsiher: Elsevier
Total Pages: 504
Release: 2007-09-04
Genre: Mathematics
ISBN: 0080560709

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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
Author: Ioannis Konstantinos Argyros,Saïd Hilout
Publsiher: Polimetrica s.a.s.
Total Pages: 571
Release: 2009
Genre: Mathematics
ISBN: 9788876991516

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Iterative Methods and Their Dynamics with Applications

Iterative Methods and Their Dynamics with Applications
Author: Ioannis Konstantinos Argyros,Angel Alberto Magreñán
Publsiher: CRC Press
Total Pages: 365
Release: 2017-07-12
Genre: Mathematics
ISBN: 9781498763622

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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.

A Contemporary Study of Iterative Methods

A Contemporary Study of Iterative Methods
Author: A. Alberto Magrenan,Ioannis Argyros
Publsiher: Academic Press
Total Pages: 400
Release: 2018-02-13
Genre: Mathematics
ISBN: 9780128094938

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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 Computations Theory and Algorithms

Numerical Computations  Theory and Algorithms
Author: Yaroslav D. Sergeyev,Dmitri E. Kvasov
Publsiher: Springer Nature
Total Pages: 622
Release: 2020-02-13
Genre: Computers
ISBN: 9783030390815

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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.

The Theory and Applications of Iteration Methods

The Theory and Applications of Iteration Methods
Author: Ioannis K. Argyros
Publsiher: CRC Press
Total Pages: 470
Release: 2022-01-21
Genre: Mathematics
ISBN: 9781000536775

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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
Author: George A. Anastassiou,Ioannis K. Argyros
Publsiher: Springer
Total Pages: 161
Release: 2017-10-27
Genre: Technology & Engineering
ISBN: 9783319695266

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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.

Numerical Methods in Computational Mechanics

Numerical Methods in Computational Mechanics
Author: Jamshid Ghaboussi,Xiping Steven Wu
Publsiher: CRC Press
Total Pages: 331
Release: 2016-11-25
Genre: Mathematics
ISBN: 9781315351643

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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.