April 14, 2021

## Dynamical Systems Method for Solving Nonlinear Operator Equations

Author : Alexander G. Ramm
Publisher : Elsevier
Release Date : 2006-09-25
Category : Mathematics
Total pages :304

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

Author : Alexander G. Ramm,Nguyen S. Hoang
Publisher : John Wiley & Sons
Release Date : 2013-06-07
Category : Mathematics
Total pages :576

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

Author : Anonim
Publisher : Unknown
Release Date : 2021
Category :
Total pages :129

## Information Computing and Applications

Author : Chunfeng Liu,Jincai Chang,Aimin Yang
Publisher : Springer Science & Business Media
Release Date : 2011-12-05
Category : Computers
Total pages :716

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.

## Methods of Hilbert Spaces in the Theory of Nonlinear Dynamical Systems

Author : K Kowalski
Publisher : World Scientific
Release Date : 1994-07-26
Category : Medical
Total pages :140

This book is the first monograph on a new powerful method discovered by the author for the study of nonlinear dynamical systems relying on reduction of nonlinear differential equations to the linear abstract Schrödinger-like equation in Hilbert space. Besides the possibility of unification of many apparently completely different techniques, the “quantal” Hilbert space formalism introduced enables new original methods to be discovered for solving nonlinear problems arising in investigation of ordinary and partial differential equations as well as difference equations. Applications covered in the book include symmetries and first integrals, linearization transformations, Bäcklund transformations, stroboscopic maps, functional equations involving the case of Feigenbaum-Cvitanovic renormalization equations and chaos. Contents:IntroductionOrdinary Differential Equations:Evolution Equation in Hilbert SpaceOperator Evolution EquationsSymmetries and First IntegralsAlternative Linearization ApproachesPartial Differential Equations:Evolution Equation in Hilbert SpaceOperator Evolution EquationsSymmetries and First IntegralsDifference Equations:Evolution Equation in Hilbert SpaceOperator Evolution EquationsFunctional EquationsApplications:First IntegralsLinearization TransformationsBäcklund TransformationsFeigenbaum-Cvitanovic Renormalization EquationsChaosAppendices:Hilbert SpacesQuantum MechanicsBose Operators and Coherent StatesPosition and Momentum OperatorsFunctional DerivativeBibliographySymbol IndexSubject Index Readership: Researchers in the field of nonlinear dynamical systems and advanced graduate students. keywords:Nonlinear Dynamical Systems;Classical Mechanics;Carleman Linearization;Koopman Approach;Hilbert Space “… a systematic and detailed presentation of the Hilbert space approach to the theory of nonlinear dynamical systems, a far-reaching generalization of the Carleman embedding.” Mathematical Reviews

## Mathematical Reviews

Author : Anonim
Publisher : Unknown
Release Date : 2006
Category : Mathematics
Total pages :129

## Annales Polonici Mathematici

Author : Anonim
Publisher : Unknown
Release Date : 2009
Category : Mathematics
Total pages :129

## Seventh Conference on Probability and Statistics in Atmospheric Sciences of the American Meteorological Society, November 2-6, 1981, Monterey, California

Author : Anonim
Publisher : Unknown
Release Date : 1981
Category : Meteorology
Total pages :235

## Numerical Mathematics

Author : Anonim
Publisher : Unknown
Release Date : 2007
Category : Numerical analysis
Total pages :129

## Dynamic Impulse Systems

Author : S.T. Zavalishchin,A.N. Sesekin
Publisher : Springer Science & Business Media
Release Date : 2013-03-14
Category : Mathematics
Total pages :260

A number of optimization problems of the mechanics of space flight and the motion of walking robots and manipulators, and of quantum physics, eco momics and biology, have an irregular structure: classical variational proce dures do not formally make it possible to find optimal controls that, as we explain, have an impulse character. This and other well-known facts lead to the necessity for constructing dynamical models using the concept of a gener alized function (Schwartz distribution). The problem ofthe systematization of such models is very important. In particular, the problem of the construction of the general form of linear and nonlinear operator equations in distributions is timely. Another problem is related to the proper determination of solutions of equations that have nonlinear operations over generalized functions in their description. It is well-known that "the value of a distribution at a point" has no meaning. As a result the problem to construct the concept of stability for generalized processes arises. Finally, optimization problems for dynamic systems in distributions need finding optimality conditions. This book contains results that we have obtained in the above-mentioned directions. The aim of the book is to provide for electrical and mechanical engineers or mathematicians working in applications, a general and systematic treat ment of dynamic systems based on up-to-date mathematical methods and to demonstrate the power of these methods in solving dynamics of systems and applied control problems.

## Control and Dynamic Systems

Author : Anonim
Publisher : Unknown
Release Date : 1967
Category : Automatic control
Total pages :129

## Nonlinear Dynamical Systems in Engineering

Author : Vasile Marinca,Nicolae Herisanu
Publisher : Springer Science & Business Media
Release Date : 2012-01-05
Category : Technology & Engineering
Total pages :396

This book presents and extend different known methods to solve different types of strong nonlinearities encountered by engineering systems. A better knowledge of the classical methods presented in the first part lead to a better choice of the so-called “base functions”. These are absolutely necessary to obtain the auxiliary functions involved in the optimal approaches which are presented in the second part. Every chapter introduces a distinct approximate method applicable to nonlinear dynamical systems. Each approximate analytical approach is accompanied by representative examples related to nonlinear dynamical systems from to various fields of engineering.

## Integral Equations, Boundary Value Problems and Related Problems

Author : Xing Li
Publisher : World Scientific
Release Date : 2013
Category : Mathematics
Total pages :285

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.

## Random Fields Estimation

Author : Alexander G. Ramm
Publisher : World Scientific
Release Date : 2005
Category : Technology & Engineering
Total pages :373

This book contains a novel theory of random fields estimation of Wiener type, developed originally by the author and presented here. No assumption about the Gaussian or Markovian nature of the fields are made. The theory, constructed entirely within the framework of covariance theory, is based on a detailed analytical study of a new class of multidimensional integral equations basic in estimation theory.This book is suitable for graduate courses in random fields estimation. It can also be used in courses in functional analysis, numerical analysis, integral equations, and scattering theory.

## Differential Operator Equations

Author : Alekseĭ Alekseevich Dezin
Publisher : Unknown
Release Date : 2000
Category : Boundary value problems
Total pages :161