Polynomial Operator Equations in Abstract Spaces and Applications: in Abstract Spaces and Applications

Science & Math

Argyros, Ioannis K.

Mathematics

CRC-Press

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.

The Theory and Applications of Iteration Methods

Computers & Technology

Computer Science

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.

Convergence and Applications of Newton-type Iterations

Springer

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.

The Theory and Applications of Iteration Methods (Systems Engineering)

Szidarovszky, Ferenc

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: 
<li>Special cases of nonlinear operator equations 
</li>
<li>Solution of polynomial operator equations of positive integer degree n 
</li>
<li>Results on global existence theorems not related with contractions 
</li>
<li>Galois theory 
</li>
<li>Polynomial integral and polynomial differential equations appearing in radiative transfer, heat transfer, neutron transport, electromechanical networks, elasticity, and other areas 
</li>
<li>Results on the various Chandrasekhar equations 
</li>
<li>Weierstrass theorem 
</li>
<li>Matrix representations 
</li>
<li>Lagrange and Hermite interpolation 
</li>
<li>Bounds of polynomial equations in Banach space, Banach algebra, and Hilbert space The materials discussed can be used for the following studies 
</li>
<li>Advanced numerical analysis 
</li>
<li>Numerical functional analysis 
</li>
<li>Functional analysis 
</li>
<li>Approximation theory 
</li>
<li>Integral and differential equations Tables include 
</li>
<li>Numerical solutions for Chandrasekhar's equation I to VI 
</li>
<li>Error bounds comparison 
</li>
<li>Accelerations schemes I and II for Newton's method 
</li>
<li>Newton's method 
</li>
<li>Secant method The self-contained text thoroughly details results, adds exercises for each chapter, and includes several applications for the solution of integral and differential equations throughout every chapter.</li>

Mathematical Modeling for the Solution of Equations and Systems of Equations With Applications: Volume II (Mathematics Research Developments)

George, Santhosh

Thapa, Narayan

Nova Science Pub Inc

This book is dedicated to the approximation of solutions of nonlinear equations using iterative methods. The study about convergence matter of iterative methods is usually based on two categories: semi-local and local convergence analysis. The semi-local convergence category is, based on the information around an initial point, to provide criteria ensuring the convergence of the method; while the local one is, based on the information around a solution, to find estimates of the radii of the convergence balls. The book is divided into two volumes. The chapters in each volume are self-contained so they can be read independently. Each chapter contains semi-local and local convergence results for single, multi-step and multi-point old and new contemporary iterative methods involving Banach, Hilbert or Euclidean valued operators. These methods are used to generate a sequence defined on the aforementioned spaces that converges with a solution of a nonlinear equation, an inverse problem or an ill-posed problem. It is worth mentioning that most problems in computational and related disciplines can be brought in the form of an equation using mathematical modelling. The solutions of equations can be found in analytical form only in special cases. Hence, it is very important to study the convergence of iterative methods. The book is a valuable tool for researchers, practitioners, graduate students, and can also be used as a textbook for seminars in all computational and related disciplines.

Mathematical Modeling for the Solution of Equations and Systems of Equations With Applications (Mathematics Research Developments)

Mathematical Modeling for the Solution of Equations and Systems of Equations With Applications

This book is intended for undergraduate and graduate researchers and practitioners in computational sciences and as a reference book for an advanced computational methods course. We have included new results for iterative procedures in abstract spaces general enough for handling inverse problems in various situations related to real-life problems through mathematical modeling. The book contains a plethora of updated bibliography and provides comparison between various investigations made in recent years in the field of computational mathematics in the wide sense. Iterative processes are the tools used to generate sequences approximating solutions of equations describing the real-life problems stated above and others originating from Biosciences, Engineering, Mathematical Economics, Mathematical Biology, Mathematical Chemistry, Mathematical Physics Medicine, Mathematical Programming, and other disciplines. The book also provides recent advancements on the study of iterative procedures and can be used as a source from which one can obtain the proper method to use in order to solve a problem. The book requires a fundamental background in Mathematical Statistics, Linear Algebra and Numerical Analysis. It may be used as a self-study reference or as a supplementary text for an advanced course in Biosciences, Engineering and Computational Sciences.

Undergraduate Research at Cameron University on Iterative Procedures in Banach and Other Spaces

The exponential growth of technology forces all disciplines to adjust accordingly, so they can meet the demands of a very dynamic world that heavily depends upon it. Therefore, mathematics cannot be an exception. In fact, mathematics should be the first to adjust and in fact it is. In this volume, which is a continuation of the previous three under the same title, we present state-of-the-art iterative methods for solving equations related to concrete problems from diverse areas such as applied mathematics, mathematical: biology, chemistry, economics, physics and also engineering to mention a few. Most of these methods are new and a few are old but still very popular. One major problem with iterative methods is that the convergence domain is small in general. We have introduced a technique that finds a smaller set than before containing the iterates leading to tighter Lipschitz functions than before. This way and under the same computational effort, we derive: weaker sufficient convergence criteria (leading to a wider choice of initial points); tighter error bounds on the distances involved (i.e., fewer iterates are needed to obtain a desired predetermined accuracy), and a more precise information on the location of the solution. These advantages are considered major achievements in computational disciplines. The volume requires knowledge of linear algebra, numerical functional analysis and familiarity with contemporary computing programing. It can be used by researchers, practitioners, senior undergraduate and graduate students as a source material or as a required textbook in the classroom.

See the best price to sell, buy, or rent books by Argyros, Ioannis K.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Argyros, Ioannis K.

See the best price to sell, buy, or rent books by Argyros, Ioannis K.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Polynomial Operator Equations in Abstract Spaces and Applications: in Abstract Spaces and Applications

The Theory and Applications of Iteration Methods

Convergence and Applications of Newton-type Iterations

The Theory and Applications of Iteration Methods (Systems Engineering)

Polynomial Operator Equations in Abstract Spaces and Applications: in Abstract Spaces and Applications

Mathematical Modeling for the Solution of Equations and Systems of Equations With Applications: Volume II (Mathematics Research Developments)

Mathematical Modeling for the Solution of Equations and Systems of Equations With Applications (Mathematics Research Developments)

Mathematical Modeling for the Solution of Equations and Systems of Equations With Applications

Undergraduate Research at Cameron University on Iterative Procedures in Banach and Other Spaces

Mathematical Modeling for the Solution of Equations and Systems of Equations With Applications