Ioannis K Argyros's Books

The Theory and Applications of Iteration Methods

By: Ioannis K. Argyros

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The Theory and Applications of Iteration Methods

By: Ioannis K. Argyros

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.

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471

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CRC Press

Published Date

ISBN 10

1000536750

ISBN 13

9781000536751

Newton Methods

By: Ioannis K. Argyros

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Newton Methods

By: Ioannis K. Argyros

This self-contained treatment offers a contemporary and systematic development of the theory and application of Newton methods, which are undoubtedly the most effective tools for solving equations appearing in computational sciences. Its focal point resides in an exhaustive analysis of the convergence properties of several Newton variants used in connection to specific real life problems originated from astrophysics, engineering, mathematical economics and other applied areas. What distinguishes this book from others is the fact that the weak convergence conditions inaugurated here allow for a wider applicability of Newton methods; finer error bounds on the distances involved, and a more precise information on the location of the solution. These factors make this book ideal for researchers, practitioners and students.

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422

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Nova Publishers

Published Date

ISBN 10

1594540527

ISBN 13

9781594540523

Research in Mathematics at Cameron University

By: Ioannis K. Argyros

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Research in Mathematics at Cameron University

By: Ioannis K. Argyros

Numerous problems from diverse disciplines can be converted using mathematical modeling to an equation defined on suitable abstract spaces usually involving the n-dimensional Euclidean space or Hilbert space or Banach Space or even more general spaces. The solution of these equations is sought in closed form. But this is possible only in special cases. That is why researchers and practitioners use iterative algorithms, which seem to be the only alternative.Due to the explosion of technology, faster and faster computers become available. This development simply means that new optimized algorithms should be developed to take advantage of these improvements. That is exactly where we come in with our book containing such algorithms with applications in problems from numerical analysis and economics but also from other areas such as biology, chemistry, physics, parallel computing, and engineering. The book is an outgrowth of scientific research conducted over two years. This book can be used by senior undergraduate students, graduate students, researchers, and practitioners in the aforementioned areas in the classroom or as reference material. Readers should know the fundamentals of numerical-functional analysis, economic theory, and Newtonian physics. Some knowledge of computers and contemporary programming shall be very helpful to readers.

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ISBN 10

1536194174

ISBN 13

9781536194173

Numerical Methods for Equations and its Applications

By: Ioannis K. Argyros,Yeol J. Cho,Saïd Hilout

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Numerical Methods for Equations and its Applications

By: Ioannis K. Argyros,Yeol J. Cho,Saïd Hilout

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 contains several new theoretical results and important applications in engineering, in dynamic economics systems, in input-output system, in the solution of nonlinear and linear differential equations, and optimization problem.

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476

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CRC Press

Published Date

ISBN 10

1578087538

ISBN 13

9781578087532

Intelligent Numerical Methods: Applications to Fractional Calculus

By: George A. Anastassiou,Ioannis K. Argyros

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Intelligent Numerical Methods: Applications to Fractional Calculus

By: George A. Anastassiou,Ioannis K. Argyros

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.

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427

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Springer

Published Date

ISBN 10

3319267213

ISBN 13

9783319267210

Functional Numerical Methods: Applications to Abstract Fractional Calculus

By: George A. Anastassiou,Ioannis K. Argyros

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Functional Numerical Methods: Applications to Abstract Fractional Calculus

By: George A. Anastassiou,Ioannis K. Argyros

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.

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166

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Springer

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ISBN 10

3319695266

ISBN 13

9783319695266

Intelligent Numerical Methods II: Applications to Multivariate Fractional Calculus

By: George A. Anastassiou,Ioannis K. Argyros

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Intelligent Numerical Methods II: Applications to Multivariate Fractional Calculus

By: George A. Anastassiou,Ioannis K. Argyros

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.

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125

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Springer

Published Date

ISBN 10

3319336061

ISBN 13

9783319336060

The Theory and Applications of Iteration Methods

By: Ioannis K. Argyros

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The Theory and Applications of Iteration Methods

By: Ioannis K. Argyros

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471

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CRC Press

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ISBN 10

1000536750

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9781000536751

Convergence and Applications of Newton-type Iterations

By: Ioannis K. Argyros

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Convergence and Applications of Newton-type Iterations

By: Ioannis K. Argyros

This monograph is devoted to a comprehensive treatment of iterative methods for solving nonlinear equations with particular emphasis on semi-local convergence analysis. Theoretical results are applied to engineering, dynamic economic systems, input-output systems, nonlinear and linear differential equations, and optimization problems. Accompanied by many exercises, some with solutions, the book may be used as a supplementary text in the classroom for an advanced course on numerical functional analysis.

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513

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Springer Science & Business Media

Published Date

ISBN 10

0387727434

ISBN 13

9780387727431

Advances In The Efficiency Of Computational Methods And Applications

By: Ioannis K Argyros

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Advances In The Efficiency Of Computational Methods And Applications

By: Ioannis K Argyros

This invaluable textbook creates a general framework for the study of optimal iterative procedures for problems that are solved approximately. Emphasis is given to the efficiency of numerical methods. For generality the setting is abstract, but the book presents many applications to practical problems, allowing the reader to take advantage of the most modern high speed calculating devices, and provides examples to illustrate concepts and major theorems. The examples are selected from astrophysics (radiative transfer and the kinetic theory of gases), mechanics (elasticity), economics (predator-prey problems), the n-dimensional Euclidean space and other applied areas. At the end of the textbook, contemporary numerical algorithms to be used for high speed computations have been included.The book will benefit not only senior undergraduates, graduate students and researchers in the field but also those who wish to obtain information about specific results or techniques that take into account the particular nature of the equation.

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560

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

9813105712

ISBN 13

9789813105713

Computational Methods In Nonlinear Analysis: Efficient Algorithms, Fixed Point Theory And Applications

By: Ioannis K Argyros,Said Hilout

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Computational Methods In Nonlinear Analysis: Efficient Algorithms, Fixed Point Theory And Applications

By: Ioannis K Argyros,Said Hilout

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 of the present book. The second goal is the applications of these methods in nonlinear problems and the connection with fixed point theory.This book is intended for researchers in computational sciences, and as a reference book for an advanced computational methods in nonlinear analysis. We collect the recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces, and present several applications and connections with fixed point theory. The book contains abundant and updated bibliography, and provides comparison between various investigations made in recent years in the field of computational nonlinear analysis.

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592

Publisher

World Scientific

Published Date

ISBN 10

9814405841

ISBN 13

9789814405843

Iterative Methods and Their Dynamics with Applications

A Contemporary Study

By: Ioannis Konstantinos Argyros,Angel Alberto Magreñán

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Iterative Methods and Their Dynamics with Applications

A Contemporary Study

By: Ioannis Konstantinos Argyros,Angel Alberto Magreñán

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.

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301

Publisher

CRC Press

Published Date

ISBN 10

1351649507

ISBN 13

9781351649506

Polynomial Operator Equations in Abstract Spaces and Applications

By: Ioannis K. Argyros

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Polynomial Operator Equations in Abstract Spaces and Applications

By: Ioannis K. Argyros

Polynomial operators are a natural generalization of linear operators. Equations in such operators are the linear space analog of ordinary polynomials in one or several variables over the fields of real or complex numbers. Such equations encompass a broad spectrum of applied problems including all linear equations. Often the polynomial nature of many nonlinear problems goes unrecognized by researchers. This is more likely due to the fact that polynomial operators - unlike polynomials in a single variable - have received little attention. Consequently, this comprehensive presentation is needed, benefiting those working in the field as well as those seeking information about specific results or techniques. Polynomial Operator Equations in Abstract Spaces and Applications - an outgrowth of fifteen years of the author's research work - presents new and traditional results about polynomial equations as well as analyzes current iterative methods for their numerical solution in various general space settings. Topics include: Special cases of nonlinear operator equations Solution of polynomial operator equations of positive integer degree n Results on global existence theorems not related with contractions Galois theory Polynomial integral and polynomial differential equations appearing in radiative transfer, heat transfer, neutron transport, electromechanical networks, elasticity, and other areas Results on the various Chandrasekhar equations Weierstrass theorem Matrix representations Lagrange and Hermite interpolation Bounds of polynomial equations in Banach space, Banach algebra, and Hilbert space The materials discussed can be used for the following studies Advanced numerical analysis Numerical functional analysis Functional analysis Approximation theory Integral and differential equation

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586

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CRC Press

Published Date

ISBN 10

1000099431

ISBN 13

9781000099430

A Contemporary Study of Iterative Methods

Convergence, Dynamics and Applications

By: A. Alberto Magrenan,Ioannis Argyros

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A Contemporary Study of Iterative Methods

Convergence, Dynamics and Applications

By: A. Alberto Magrenan,Ioannis Argyros

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

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402

Publisher

Academic Press

Published Date

ISBN 10

0128094931

ISBN 13

9780128094938

Approximate Solution Of Operator Equations With Applications

By: Ioannis K Argyros

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Approximate Solution Of Operator Equations With Applications

By: Ioannis K Argyros

Researchers are faced with the problem of solving a variety of equations in the course of their work in engineering, economics, physics, and the computational sciences. This book focuses on a new and improved local-semilocal and monotone convergence analysis of efficient numerical methods for computing approximate solutions of such equations, under weaker hypotheses than in other works. This particular feature is the main strength of the book when compared with others already in the literature.The explanations and applications in the book are detailed enough to capture the interest of curious readers and complete enough to provide the necessary background material to go further into the subject.

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527

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

9813106549

ISBN 13

9789813106543

Newton Methods

By: Ioannis K. Argyros

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Newton Methods

By: Ioannis K. Argyros

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422

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Nova Publishers

Published Date

ISBN 10

1594540527

ISBN 13

9781594540523

Computational Theory of Iterative Methods

By: Ioannis Argyros

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Computational Theory of Iterative Methods

By: Ioannis Argyros

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

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505

Publisher

Elsevier

Published Date

ISBN 10

0080560709

ISBN 13

9780080560700

Intelligent Numerical Methods: Applications to Fractional Calculus

By: George A. Anastassiou,Ioannis K. Argyros

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Intelligent Numerical Methods: Applications to Fractional Calculus

By: George A. Anastassiou,Ioannis K. Argyros

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Page Count

427

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Springer

Published Date

ISBN 10

3319267213

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9783319267210

Iterative Methods and Their Dynamics with Applications

A Contemporary Study

By: Ioannis Konstantinos Argyros,Angel Alberto Magreñán

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Iterative Methods and Their Dynamics with Applications

A Contemporary Study

By: Ioannis Konstantinos Argyros,Angel Alberto Magreñán

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301

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CRC Press

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ISBN 10

1351649507

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9781351649506

Intelligent Numerical Methods II: Applications to Multivariate Fractional Calculus

By: George A. Anastassiou,Ioannis K. Argyros

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Intelligent Numerical Methods II: Applications to Multivariate Fractional Calculus

By: George A. Anastassiou,Ioannis K. Argyros

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125

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Springer

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3319336061

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9783319336060

Advances In The Efficiency Of Computational Methods And Applications

By: Ioannis K Argyros

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Advances In The Efficiency Of Computational Methods And Applications

By: Ioannis K Argyros

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560

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World Scientific Publishing Company

Published Date

ISBN 10

9813105712

ISBN 13

9789813105713

The Theory and Applications of Iteration Methods

By: Ioannis K. Argyros,Ferenc Szidarovszky

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The Theory and Applications of Iteration Methods

By: Ioannis K. Argyros,Ferenc Szidarovszky

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.

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368

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CRC Press

Published Date

ISBN 10

1351408984

ISBN 13

9781351408981

Convergence and Applications of Newton-type Iterations

By: Ioannis K. Argyros

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Convergence and Applications of Newton-type Iterations

By: Ioannis K. Argyros

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513

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Springer Science & Business Media

Published Date

ISBN 10

0387727434

ISBN 13

9780387727431

Functional Numerical Methods: Applications to Abstract Fractional Calculus

By: George A. Anastassiou,Ioannis K. Argyros

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Functional Numerical Methods: Applications to Abstract Fractional Calculus

By: George A. Anastassiou,Ioannis K. Argyros

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Page Count

166

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Springer

Published Date

ISBN 10

3319695266

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9783319695266

Computational Methods In Nonlinear Analysis: Efficient Algorithms, Fixed Point Theory And Applications

By: Ioannis K Argyros,Said Hilout

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Computational Methods In Nonlinear Analysis: Efficient Algorithms, Fixed Point Theory And Applications

By: Ioannis K Argyros,Said Hilout

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592

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World Scientific

Published Date

ISBN 10

9814405841

ISBN 13

9789814405843

Polynomial Operator Equations in Abstract Spaces and Applications

By: Ioannis K. Argyros

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Polynomial Operator Equations in Abstract Spaces and Applications

By: Ioannis K. Argyros

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598

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CRC Press

Published Date

ISBN 10

1000142450

ISBN 13

9781000142457

Mathematical Modelling with Applications in Biosciences and Engineering

By: Ioannis K. Argyros,Saïd Hilout,Mohammad A. Tabatabai

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Mathematical Modelling with Applications in Biosciences and Engineering

By: Ioannis K. Argyros,Saïd Hilout,Mohammad A. Tabatabai

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361

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ISBN 10

1617616397

ISBN 13

9781617616396

Approximate Solution of Operator Equations with Applications

By: Ioannis K. Argyros

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Approximate Solution of Operator Equations with Applications

By: Ioannis K. Argyros

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530

Publisher

World Scientific

Published Date

ISBN 10

9812563652

ISBN 13

9789812563651

Contemporary Algorithms for Solving Problems in Economics and Other Disciplines

By: Ioannis K. Argyros

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Contemporary Algorithms for Solving Problems in Economics and Other Disciplines

By: Ioannis K. Argyros

Numerous problems from diverse disciplines can be converted using mathematical modeling to an equation defined on suitable abstract spaces usually involving the n-dimensional Euclidean space or Hilbert space or Banach Space or even more general spaces. The solution of these equations is sought in closed form. But this is possible only in special cases. That is why researchers and practitioners use algorithms which seems to be the only alternative. Due to the explosion of technology, scientific and parallel computing, faster and faster computers become available. This development simply means that new optimized algorithms should be developed to take advantage of these improvements. There is exactly where we come in with our book containing such algorithms with application especially in problems from Economics but also from other areas such as Mathematical: Biology, Chemistry, Physics, Scientific, Parallel Computing, and also Engineering. The book can be used by senior undergraduate students, graduate students, researchers and practitioners in the aforementioned area in the class room or as a reference material. Readers should know the fundamentals of numerical functional analysis, economic theory, and Newtonian physics. Some knowledge of computers and contemporary programming shall be very helpful to the readers.

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Page Count

325

Published Date

ISBN 10

1536181285

ISBN 13

9781536181289

Advances on Iterative Procedures

By: Ioannis K. Argyros

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Advances on Iterative Procedures

By: Ioannis K. Argyros

From the preface. The monograph is intended for senior undergraduate students, graduate students, researchers, practitioners in computational mathematics and applied sciences. It can also be used as a reference book for an advanced numerical-functional analysis course. The goal is to introduce these powerful concepts and techniques at the earliest possible stage. 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.

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Page Count

412

Published Date

ISBN 10

1536112755

ISBN 13

9781536112757

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