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Author: Ioannis K. Argyros
Publisher:
ISBN: 9781536133615
Category :
Languages : en
Pages : 441
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Book Description
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.
Author: Ioannis K. Argyros
Publisher:
ISBN: 9781536133622
Category : MATHEMATICS
Languages : en
Pages : 336
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Book Description
Author: Ioannis K. Argyros
Publisher:
ISBN: 9781536174748
Category :
Languages : en
Pages : 633
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Book Description
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.
Author: Ioannis K. Argyros
Publisher:
ISBN: 9781536133615
Category :
Languages : en
Pages : 441
Get Book
Book Description
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.
Author: Ioannis K. Argyros
Publisher:
ISBN: 9781536133103
Category : MATHEMATICS
Languages : en
Pages :
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Book Description
Author: Sandip Banerjee
Publisher: CRC Press
ISBN: 1482229161
Category : Mathematics
Languages : en
Pages : 276
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Book Description
Almost every year, a new book on mathematical modeling is published, so, why another? The answer springs directly from the fact that it is very rare to find a book that covers modeling with all types of differential equations in one volume. Until now. Mathematical Modeling: Models, Analysis and Applications covers modeling with all kinds of differe
Author: Alan Tucker
Publisher: MacMillan Publishing Company
ISBN:
Category : Algebras, Linear
Languages : en
Pages : 570
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Book Description
Author: Albert C.J. Luo
Publisher: Springer
ISBN: 3319266306
Category : Technology & Engineering
Languages : en
Pages : 205
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Book Description
The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems.
Author: Edward A. Bender
Publisher: Courier Corporation
ISBN: 0486137120
Category : Mathematics
Languages : en
Pages : 273
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Book Description
Employing a practical, "learn by doing" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields — including science, engineering, and operations research — to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The lively and accessible text requires only minimal scientific background. Designed for senior college or beginning graduate-level students, it assumes only elementary calculus and basic probability theory for the first part, and ordinary differential equations and continuous probability for the second section. All problems require students to study and create models, encouraging their active participation rather than a mechanical approach. Beyond the classroom, this volume will prove interesting and rewarding to anyone concerned with the development of mathematical models or the application of modeling to problem solving in a wide array of applications.
Author: Jonas Hall
Publisher: John Wiley & Sons
ISBN: 1119102693
Category : Mathematics
Languages : en
Pages : 568
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Book Description
A logical problem-based introduction to the use of GeoGebra for mathematical modeling and problem solving within various areas of mathematics A well-organized guide to mathematical modeling techniques for evaluating and solving problems in the diverse field of mathematics, Mathematical Modeling: Applications with GeoGebra presents a unique approach to software applications in GeoGebra and WolframAlpha. The software is well suited for modeling problems in numerous areas of mathematics including algebra, symbolic algebra, dynamic geometry, three-dimensional geometry, and statistics. Featuring detailed information on how GeoGebra can be used as a guide to mathematical modeling, the book provides comprehensive modeling examples that correspond to different levels of mathematical experience, from simple linear relations to differential equations. Each chapter builds on the previous chapter with practical examples in order to illustrate the mathematical modeling skills necessary for problem solving. Addressing methods for evaluating models including relative error, correlation, square sum of errors, regression, and confidence interval, Mathematical Modeling: Applications with GeoGebra also includes: Over 400 diagrams and 300 GeoGebra examples with practical approaches to mathematical modeling that help the reader develop a full understanding of the content Numerous real-world exercises with solutions to help readers learn mathematical modeling techniques A companion website with GeoGebra constructions and screencasts Mathematical Modeling: Applications with GeoGebrais ideal for upper-undergraduate and graduate-level courses in mathematical modeling, applied mathematics, modeling and simulation, operations research, and optimization. The book is also an excellent reference for undergraduate and high school instructors in mathematics.
Author: Mark McKibben
Publisher: CRC Press
ISBN: 1466557079
Category : Mathematics
Languages : en
Pages : 500
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Book Description
A unique textbook for an undergraduate course on mathematical modeling, Differential Equations with MATLAB: Exploration, Applications, and Theory provides students with an understanding of the practical and theoretical aspects of mathematical models involving ordinary and partial differential equations (ODEs and PDEs). The text presents a unifying picture inherent to the study and analysis of more than 20 distinct models spanning disciplines such as physics, engineering, and finance. The first part of the book presents systems of linear ODEs. The text develops mathematical models from ten disparate fields, including pharmacokinetics, chemistry, classical mechanics, neural networks, physiology, and electrical circuits. Focusing on linear PDEs, the second part covers PDEs that arise in the mathematical modeling of phenomena in ten other areas, including heat conduction, wave propagation, fluid flow through fissured rocks, pattern formation, and financial mathematics. The authors engage students by posing questions of all types throughout, including verifying details, proving conjectures of actual results, analyzing broad strokes that occur within the development of the theory, and applying the theory to specific models. The authors’ accessible style encourages students to actively work through the material and answer these questions. In addition, the extensive use of MATLAB® GUIs allows students to discover patterns and make conjectures.
