A Contemporary Study Of Iterative Methods
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Author | : A. Alberto Magrenan |
Publisher | : Academic Press |
Total Pages | : 402 |
Release | : 2018-02-13 |
Genre | : Mathematics |
ISBN | : 0128094931 |
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
Author | : Yousef Saad |
Publisher | : SIAM |
Total Pages | : 537 |
Release | : 2003-04-01 |
Genre | : Mathematics |
ISBN | : 0898715342 |
Mathematics of Computing -- General.
Author | : Juan R. Torregrosa |
Publisher | : MDPI |
Total Pages | : 494 |
Release | : 2019-12-06 |
Genre | : Mathematics |
ISBN | : 3039219405 |
Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a non-trivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.
Author | : Ioannis K. Argyros |
Publisher | : CRC Press |
Total Pages | : 356 |
Release | : 2022-01-21 |
Genre | : Mathematics |
ISBN | : 1000536777 |
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.
Author | : Harendra Singh |
Publisher | : CRC Press |
Total Pages | : 337 |
Release | : 2021-07-29 |
Genre | : Technology & Engineering |
ISBN | : 1000381080 |
Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models. This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and science. Engineers, mathematicians, scientists, and researchers working on real-life mathematical problems will find this book useful.
Author | : Ioannis Konstantinos Argyros |
Publisher | : CRC Press |
Total Pages | : 366 |
Release | : 2017-07-12 |
Genre | : Mathematics |
ISBN | : 1498763626 |
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.
Author | : Tatsien Li |
Publisher | : World Scientific |
Total Pages | : 306 |
Release | : 2004-07-26 |
Genre | : Mathematics |
ISBN | : 9814482145 |
This invaluable volume is a collection of articles in memory of Jacques-Louis Lions, a leading mathematician and the founder of the Contemporary French Applied Mathematics School. The contributions have been written by his friends, colleagues and students, including C Bardos, A Bensoussan, S S Chern, P G Ciarlet, R Glowinski, Gu Chaohao, B Malgrange, G Marchuk, O Pironneau, W Strauss, R Temam, etc.The book concerns many important results in analysis, geometry, numerical methods, fluid mechanics, control theory, etc.
Author | : Azmy S. Ackleh |
Publisher | : CRC Press |
Total Pages | : 628 |
Release | : 2009-07-20 |
Genre | : Mathematics |
ISBN | : 1420091581 |
Classical and Modern Numerical Analysis: Theory, Methods and Practice provides a sound foundation in numerical analysis for more specialized topics, such as finite element theory, advanced numerical linear algebra, and optimization. It prepares graduate students for taking doctoral examinations in numerical analysis.The text covers the main areas o
Author | : Lap Chi Lau |
Publisher | : Cambridge University Press |
Total Pages | : 255 |
Release | : 2011-04-18 |
Genre | : Computers |
ISBN | : 1139499394 |
With the advent of approximation algorithms for NP-hard combinatorial optimization problems, several techniques from exact optimization such as the primal-dual method have proven their staying power and versatility. This book describes a simple and powerful method that is iterative in essence and similarly useful in a variety of settings for exact and approximate optimization. The authors highlight the commonality and uses of this method to prove a variety of classical polyhedral results on matchings, trees, matroids and flows. The presentation style is elementary enough to be accessible to anyone with exposure to basic linear algebra and graph theory, making the book suitable for introductory courses in combinatorial optimization at the upper undergraduate and beginning graduate levels. Discussions of advanced applications illustrate their potential for future application in research in approximation algorithms.
Author | : Ioannis K. Argyros |
Publisher | : Nova Publishers |
Total Pages | : 422 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 9781594540523 |
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.