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Dynamical Systems Method For Solving Operator Equations

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Dynamical Systems Method for Solving Nonlinear Operator Equations

Dynamical Systems Method for Solving Nonlinear Operator Equations Book
Author : Alexander G. Ramm
Publisher : Elsevier
Release : 2006-09-25
ISBN : 9780080465562
Language : En, Es, Fr & De

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Book Description :

Dynamical Systems Method for Solving Nonlinear Operator Equations is of interest to graduate students in functional analysis, numerical analysis, and ill-posed and inverse problems especially. The book presents a general method for solving operator equations, especially nonlinear and ill-posed. It requires a fairly modest background and is essentially self-contained. All the results are proved in the book, and some of the background material is also included. The results presented are mostly obtained by the author. Contains a systematic development of a novel general method, the dynamical systems method, DSM for solving operator equations, especially nonlinear and ill-posed Self-contained, suitable for wide audience Can be used for various courses for graduate students and partly for undergraduates (especially for RUE classes)

Dynamical Systems Method and Applications

Dynamical Systems Method and Applications Book
Author : Alexander G. Ramm,Nguyen S. Hoang
Publisher : John Wiley & Sons
Release : 2013-06-07
ISBN : 111819960X
Language : En, Es, Fr & De

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Book Description :

Demonstrates the application of DSM to solve a broad range of operator equations The dynamical systems method (DSM) is a powerful computational method for solving operator equations. With this book as their guide, readers will master the application of DSM to solve a variety of linear and nonlinear problems as well as ill-posed and well-posed problems. The authors offer a clear, step-by-step, systematic development of DSM that enables readers to grasp the method's underlying logic and its numerous applications. Dynamical Systems Method and Applications begins with a general introduction and then sets forth the scope of DSM in Part One. Part Two introduces the discrepancy principle, and Part Three offers examples of numerical applications of DSM to solve a broad range of problems in science and engineering. Additional featured topics include: General nonlinear operator equations Operators satisfying a spectral assumption Newton-type methods without inversion of the derivative Numerical problems arising in applications Stable numerical differentiation Stable solution to ill-conditioned linear algebraic systems Throughout the chapters, the authors employ the use of figures and tables to help readers grasp and apply new concepts. Numerical examples offer original theoretical results based on the solution of practical problems involving ill-conditioned linear algebraic systems, and stable differentiation of noisy data. Written by internationally recognized authorities on the topic, Dynamical Systems Method and Applications is an excellent book for courses on numerical analysis, dynamical systems, operator theory, and applied mathematics at the graduate level. The book also serves as a valuable resource for professionals in the fields of mathematics, physics, and engineering.

Spectral Theory and Nonlinear Analysis with Applications to Spatial Ecology

Spectral Theory and Nonlinear Analysis with Applications to Spatial Ecology Book
Author : Anonim
Publisher : Unknown
Release : 2022-08-17
ISBN : 9814479268
Language : En, Es, Fr & De

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Book Description :

Download Spectral Theory and Nonlinear Analysis with Applications to Spatial Ecology book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Information Computing and Applications

Information Computing and Applications Book
Author : Chunfeng Liu,Jincai Chang,Aimin Yang
Publisher : Springer Science & Business Media
Release : 2011-12-05
ISBN : 3642275028
Language : En, Es, Fr & De

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Book Description :

The two-volume set, CCIS 243 and CCIS 244, constitutes the refereed proceedings of the Second International Conference on Information Computing and Applications, ICICA 2010, held in Qinhuangdao, China, in October 2011. The 191 papers presented in both volumes were carefully reviewed and selected from numerous submissions. They are organized in topical sections on computational statistics, social networking and computing, evolutionary computing and applications, information education and application, internet and web computing, scientific and engineering computing, system simulation computing, bio-inspired and DNA computing, internet and Web computing, multimedia networking and computing, parallel and distributed computing.

Handbook of Applications of Chaos Theory

Handbook of Applications of Chaos Theory Book
Author : Christos H. Skiadas,Charilaos Skiadas
Publisher : CRC Press
Release : 2017-12-19
ISBN : 1315356546
Language : En, Es, Fr & De

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Book Description :

In addition to explaining and modeling unexplored phenomena in nature and society, chaos uses vital parts of nonlinear dynamical systems theory and established chaotic theory to open new frontiers and fields of study. Handbook of Applications of Chaos Theory covers the main parts of chaos theory along with various applications to diverse areas. Expert contributors from around the world show how chaos theory is used to model unexplored cases and stimulate new applications. Accessible to scientists, engineers, and practitioners in a variety of fields, the book discusses the intermittency route to chaos, evolutionary dynamics and deterministic chaos, and the transition to phase synchronization chaos. It presents important contributions on strange attractors, self-exciting and hidden attractors, stability theory, Lyapunov exponents, and chaotic analysis. It explores the state of the art of chaos in plasma physics, plasma harmonics, and overtone coupling. It also describes flows and turbulence, chaotic interference versus decoherence, and an application of microwave networks to the simulation of quantum graphs. The book proceeds to give a detailed presentation of the chaotic, rogue, and noisy optical dissipative solitons; parhelic-like circle and chaotic light scattering; and interesting forms of the hyperbolic prism, the Poincaré disc, and foams. It also covers numerous application areas, from the analysis of blood pressure data and clinical digital pathology to chaotic pattern recognition to economics to musical arts and research.

Inverse Problems

Inverse Problems Book
Author : Alexander G. Ramm
Publisher : Springer Science & Business Media
Release : 2006-01-20
ISBN : 0387232184
Language : En, Es, Fr & De

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Book Description :

Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.

Integral Equations Boundary Value Problems and Related Problems

Integral Equations  Boundary Value Problems and Related Problems Book
Author : Xing Li
Publisher : World Scientific
Release : 2013
ISBN : 9814452882
Language : En, Es, Fr & De

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Book Description :

In this volume, we report new results about various theories and methods of integral equation, boundary value problems for partial differential equations and functional equations, and integral operators including singular integral equations, applications of boundary value problems and integral equations to mechanics and physics, numerical methods of integral equations and boundary value problems, theories and methods for inverse problems of mathematical physics, Clifford analysis and related problems.

Numerical Methods for Equations and its Applications

Numerical Methods for Equations and its Applications Book
Author : Ioannis K. Argyros,Yeol J. Cho,Saïd Hilout
Publisher : CRC Press
Release : 2012-06-05
ISBN : 1578087538
Language : En, Es, Fr & De

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Book Description :

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.

Computational Methods in Nonlinear Analysis

Computational Methods in Nonlinear Analysis Book
Author : Ioannis K. Argyros,Sa‹d Hilout
Publisher : World Scientific
Release : 2013
ISBN : 9814405833
Language : En, Es, Fr & De

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Book Description :

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.

Annales Polonici Mathematici

Annales Polonici Mathematici Book
Author : Anonim
Publisher : Unknown
Release : 2009
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Annales Polonici Mathematici book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Numerical Time Dependent Partial Differential Equations for Scientists and Engineers

Numerical Time Dependent Partial Differential Equations for Scientists and Engineers Book
Author : Moysey Brio,Gary M. Webb,Aramais R. Zakharian
Publisher : Academic Press
Release : 2010-09-21
ISBN : 9780080917047
Language : En, Es, Fr & De

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Book Description :

It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc. The first three chapters focus on basic properties of partial differential equations, including analysis of the dispersion relation, symmetries, particular solutions and instabilities of the PDEs; methods of discretization and convergence theory for initial value problems. The goal is to progress from observations of simple numerical artifacts like diffusion, damping, dispersion, and anisotropies to their analysis and management technique, as it is not always possible to completely eliminate them. In the second part of the book we cover topics for which there are only sporadic theoretical results, while they are an integral part and often the most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to separate physics from numerics. The following topics are addressed: Implementation of transparent and absorbing boundary conditions; Practical stability analysis in the presence of the boundaries and interfaces; Treatment of problems with different temporal/spatial scales either explicit or implicit; preservation of symmetries and additional constraints; physical regularization of singularities; resolution enhancement using adaptive mesh refinement and moving meshes. Self contained presentation of key issues in successful numerical simulation Accessible to scientists and engineers with diverse background Provides analysis of the dispersion relation, symmetries, particular solutions and instabilities of the partial differential equations

Iterative Methods without Inversion

Iterative Methods without Inversion Book
Author : Anatoly Galperin
Publisher : CRC Press
Release : 2016-11-17
ISBN : 1315350742
Language : En, Es, Fr & De

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Book Description :

Iterative Methods without Inversion presents the iterative methods for solving operator equations f(x) = 0 in Banach and/or Hilbert spaces. It covers methods that do not require inversions of f (or solving linearized subproblems). The typical representatives of the class of methods discussed are Ulm’s and Broyden’s methods. Convergence analyses of the methods considered are based on Kantorovich’s majorization principle which avoids unnecessary simplifying assumptions like differentiability of the operator or solvability of the equation. These analyses are carried out under a more general assumption about degree of continuity of the operator than traditional Lipschitz continuity: regular continuity. Key Features The methods discussed are analyzed under the assumption of regular continuity of divided difference operator, which is more general and more flexible than the traditional Lipschitz continuity. An attention is given to criterions for comparison of merits of various methods and to the related concept of optimality of a method of certain class. Many publications on methods for solving nonlinear operator equations discuss methods that involve inversion of linearization of the operator, which task is highly problematic in infinite dimensions. Accessible for anyone with minimal exposure to nonlinear functional analysis.

Stochastic Modelling in Process Technology

Stochastic Modelling in Process Technology Book
Author : Herold G. Dehling,Timo Gottschalk,Alex C. Hoffmann
Publisher : Elsevier
Release : 2007-07-03
ISBN : 9780080548975
Language : En, Es, Fr & De

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Book Description :

There is an ever increasing need for modelling complex processes reliably. Computational modelling techniques, such as CFD and MD may be used as tools to study specific systems, but their emergence has not decreased the need for generic, analytical process models. Multiphase and multicomponent systems, and high-intensity processes displaying a highly complex behaviour are becoming omnipresent in the processing industry. This book discusses an elegant, but little-known technique for formulating process models in process technology: stochastic process modelling. The technique is based on computing the probability distribution for a single particle's position in the process vessel, and/or the particle's properties, as a function of time, rather than - as is traditionally done - basing the model on the formulation and solution of differential conservation equations. Using this technique can greatly simplify the formulation of a model, and even make modelling possible for processes so complex that the traditional method is impracticable. Stochastic modelling has sporadically been used in various branches of process technology under various names and guises. This book gives, as the first, an overview of this work, and shows how these techniques are similar in nature, and make use of the same basic mathematical tools and techniques. The book also demonstrates how stochastic modelling may be implemented by describing example cases, and shows how a stochastic model may be formulated for a case, which cannot be described by formulating and solving differential balance equations. Introduction to stochastic process modelling as an alternative modelling technique Shows how stochastic modelling may be succesful where the traditional technique fails Overview of stochastic modelling in process technology in the research literature Illustration of the principle by a wide range of practical examples In-depth and self-contained discussions Points the way to both mathematical and technological research in a new, rewarding field

L System Fractals

L System Fractals Book
Author : Jibitesh Mishra,Sarojananda Mishra
Publisher : Elsevier
Release : 2007-01-08
ISBN : 9780080469386
Language : En, Es, Fr & De

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Book Description :

L-System Fractals covers all the fundamental aspects of generating fractals through L-system. Also it provides insight to various researches in this area for generating fractals through L-system approach & estimating dimensions. Also it discusses various applications of L-system fractals. Fractals generated from L-System including hybrid fractals Dimension calculation for L-system fractals Images and codes for L-system fractals Research directions in the area of L-system fractals Usage of various freely downloadable tools in this area

Creating Materials with a Desired Refraction Coefficient

Creating Materials with a Desired Refraction Coefficient Book
Author : Alexander G. Ramm
Publisher : Morgan & Claypool Publishers
Release : 2017-12-20
ISBN : 1681747111
Language : En, Es, Fr & De

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Book Description :

Creating Materials with a Desired Refraction Coefficient' provides a recipe for creating materials with a desired refraction coefficient, and the many-body wave scattering problem for many small impedance bodies is solved. The physical assumptions make the multiple scattering effects essential. On the basis of this theory, a recipe for creating materials with a desired refraction coefficient is given. Technological problems are formulated which, when solved, make the theory practically applicable. The Importance of a problem of producing a small particle with a desired boundary impedance is emphasized, and inverse scattering with non-over-determined scattering data is considered.

Computational Methods for Modeling of Nonlinear Systems by Anatoli Torokhti and Phil Howlett

Computational Methods for Modeling of Nonlinear Systems by Anatoli Torokhti and Phil Howlett Book
Author : Anatoli Torokhti,Phil Howlett
Publisher : Elsevier
Release : 2007-04-11
ISBN : 9780080475387
Language : En, Es, Fr & De

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Book Description :

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. Best operator approximation Non-Lagrange interpolation Generic Karhunen-Loeve transform Generalised low-rank matrix approximation Optimal data compression Optimal nonlinear filtering

Continuous Optimization

Continuous Optimization Book
Author : V. Jeyakumar,Alexander M. Rubinov
Publisher : Springer Science & Business Media
Release : 2006-03-09
ISBN : 0387267719
Language : En, Es, Fr & De

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Book Description :

Continuous optimization is the study of problems in which we wish to opti mize (either maximize or minimize) a continuous function (usually of several variables) often subject to a collection of restrictions on these variables. It has its foundation in the development of calculus by Newton and Leibniz in the 17*^ century. Nowadys, continuous optimization problems are widespread in the mathematical modelling of real world systems for a very broad range of applications. Solution methods for large multivariable constrained continuous optimiza tion problems using computers began with the work of Dantzig in the late 1940s on the simplex method for linear programming problems. Recent re search in continuous optimization has produced a variety of theoretical devel opments, solution methods and new areas of applications. It is impossible to give a full account of the current trends and modern applications of contin uous optimization. It is our intention to present a number of topics in order to show the spectrum of current research activities and the development of numerical methods and applications.

Numerical Mathematics

Numerical Mathematics Book
Author : Anonim
Publisher : Unknown
Release : 2007
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Numerical Mathematics book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Symmetry Problems

Symmetry Problems Book
Author : Alexander G. Ramm
Publisher : Springer Nature
Release : 2022-06-01
ISBN : 303102415X
Language : En, Es, Fr & De

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Book Description :

This book gives a necessary and sufficient condition in terms of the scattering amplitude for a scatterer to be spherically symmetric. By a scatterer we mean a potential or an obstacle. It also gives necessary and sufficient conditions for a domain to be a ball if an overdetermined boundary problem for the Helmholtz equation in this domain is solvable. This includes a proof of Schiffer's conjecture, the solution to the Pompeiu problem, and other symmetry problems for partial differential equations. It goes on to study some other symmetry problems related to the potential theory. Among these is the problem of "invisible obstacles." In Chapter 5, it provides a solution to the Navier‒Stokes problem in ℝ³. The author proves that this problem has a unique global solution if the data are smooth and decaying sufficiently fast. A new a priori estimate of the solution to the Navier‒Stokes problem is also included. Finally, it delivers a solution to inverse problem of the potential theory without the standard assumptions about star-shapeness of the homogeneous bodies.

Markov Processes Feller Semigroups and Evolution Equations

Markov Processes  Feller Semigroups and Evolution Equations Book
Author : J. A. van Casteren
Publisher : World Scientific
Release : 2011
ISBN : 9814322180
Language : En, Es, Fr & De

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Book Description :

The book provides a systemic treatment of time-dependent strong Markov processes with values in a Polish space. It describes its generators and the link with stochastic differential equations in infinite dimensions. In a unifying way, where the square gradient operator is employed, new results for backward stochastic differential equations and long-time behavior are discussed in depth. The book also establishes a link between propagators or evolution families with the Feller property and time-inhomogeneous Markov processes. This mathematical material finds its applications in several branches of the scientific world, among which are mathematical physics, hedging models in financial mathematics, and population models.