Download or read book Linear Operator Equations Approximation And Regularization written by M Thamban Nair and published by World Scientific. This book was released on 2009-05-05 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not often be possible or may not be worth looking for due to physical constraints. In such situations, it is desirable to know how the so-called approximate solution approximates the exact solution, and what the error involved in such procedures would be.This book is concerned with the investigation of the above theoretical issues related to approximately solving linear operator equations. The main tools used for this purpose are basic results from functional analysis and some rudimentary ideas from numerical analysis. To make this book more accessible to readers, no in-depth knowledge on these disciplines is assumed for reading this book.

Download or read book Nonlinear Stochastic Operator Equations written by George Adomian and published by Academic Press. This book was released on 2014-05-09 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Stochastic Operator Equations deals with realistic solutions of the nonlinear stochastic equations arising from the modeling of frontier problems in many fields of science. This book also discusses a wide class of equations to provide modeling of problems concerning physics, engineering, operations research, systems analysis, biology, medicine. This text discusses operator equations and the decomposition method. This book also explains the limitations, restrictions and assumptions made in differential equations involving stochastic process coefficients (the stochastic operator case), which yield results very different from the needs of the actual physical problem. Real-world application of mathematics to actual physical problems, requires making a reasonable model that is both realistic and solvable. The decomposition approach or model is an approximation method to solve a wide range of problems. This book explains an inherent feature of real systems—known as nonlinear behavior—that occurs frequently in nuclear reactors, in physiological systems, or in cellular growth. This text also discusses stochastic operator equations with linear boundary conditions. This book is intended for students with a mathematics background, particularly senior undergraduate and graduate students of advanced mathematics, of the physical or engineering sciences.

Download or read book Approximate Solution of Operator Equations written by M.A. Krasnosel'skii and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most important chapters in modern functional analysis is the theory of approximate methods for solution of various mathematical problems. Besides providing considerably simplified approaches to numerical methods, the ideas of functional analysis have also given rise to essentially new computation schemes in problems of linear algebra, differential and integral equations, nonlinear analysis, and so on. The general theory of approximate methods includes many known fundamental results. We refer to the classical work of Kantorovich; the investigations of projection methods by Bogolyubov, Krylov, Keldysh and Petrov, much furthered by Mikhlin and Pol'skii; Tikho nov's methods for approximate solution of ill-posed problems; the general theory of difference schemes; and so on. During the past decade, the Voronezh seminar on functional analysis has systematically discussed various questions related to numerical methods; several advanced courses have been held at Voronezh Uni versity on the application of functional analysis to numerical mathe matics. Some of this research is summarized in the present monograph. The authors' aim has not been to give an exhaustive account, even of the principal known results. The book consists of five chapters.

Download or read book Equations with Involutive Operators written by Nikolai Karapetiants and published by Springer Science & Business Media. This book was released on 2001-06-21 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained title demonstrates an important interplay between abstract and concrete operator theory. Key ideas are developed in a step-by-step approach, beginning with required background and historical material, and culminating in the final chapters with state-of-the-art topics. Good examples, bibliography and index make this text a valuable classroom or reference resource.

Download or read book Linear Functional Equations Operator Approach written by Anatolij Antonevich and published by Birkhäuser. This book was released on 2012-12-06 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we shall study linear functional equations of the form m bu(x) == Lak(X)U(Qk(X)) = f(x), (1) k=l where U is an unknown function from a given space F(X) of functions on a set X, Qk: X -+ X are given mappings, ak and f are given functions. Our approach is based on the investigation of the operators given by the left-hand side of equa tion (1). In what follows such operators will be called functional operators. We will pay special attention to the spectral properties of functional operators, first of all, to invertibility and the Noether property. Since the set X, the space F(X), the mappings Qk and the coefficients ak are arbitrary, the class of operators of the form (1) is very rich and some of its individ ual representatives are related with problems arising in various areas of mathemat ics and its applications. In addition to the classical theory of functional equations, among such areas one can indicate the theory of functional-differential equations with deviating argument, the theory of nonlocal problems for partial differential equations, the theory of boundary value problems for the equation of a vibrating string and equations of mixed type, a number of problems of the general theory of operator algebras and the theory of dynamical systems, the spectral theory of au tomorphisms of Banach algebras, and other problems.

Download or read book Polynomial Operator Equations in Abstract Spaces and Applications written by Ioannis K. Argyros and published by CRC Press. This book was released on 1998-03-25 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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: Special cases of nonlinear operator equations Solution of polynomial operator equations of positive integer degree n Results on global existence theorems not related with contractions Galois theory Polynomial integral and polynomial differential equations appearing in radiative transfer, heat transfer, neutron transport, electromechanical networks, elasticity, and other areas Results on the various Chandrasekhar equations Weierstrass theorem Matrix representations Lagrange and Hermite interpolation Bounds of polynomial equations in Banach space, Banach algebra, and Hilbert space The materials discussed can be used for the following studies Advanced numerical analysis Numerical functional analysis Functional analysis Approximation theory Integral and differential equations Tables include Numerical solutions for Chandrasekhar's equation I to VI Error bounds comparison Accelerations schemes I and II for Newton's method Newton's method 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.

Download or read book Asymptotics of Nonlinearities and Operator Equations written by Alexander Krasnoselskii and published by Birkhäuser. This book was released on 2012-12-06 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: New methods for solving classical problems in the theory of nonlinear operator equations (solvability, multiple solutions, bifurcations, nonlinear resonance, potential methods, etc) are introduced and discussed. The general abstract theorems are illustrated by various applications to differential equations and boundary value problems. In particular, the problem on forced periodic oscillations is considered for equations arising in control theory.

Download or read book Approximate Solution Of Operator Equations With Applications written by Ioannis K Argyros and published by World Scientific Publishing Company. This book was released on 2005-08-26 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: Researchers are faced with the problem of solving a variety of equations in the course of their work in engineering, economics, physics, and the computational sciences. This book focuses on a new and improved local-semilocal and monotone convergence analysis of efficient numerical methods for computing approximate solutions of such equations, under weaker hypotheses than in other works. This particular feature is the main strength of the book when compared with others already in the literature.The explanations and applications in the book are detailed enough to capture the interest of curious readers and complete enough to provide the necessary background material to go further into the subject.

Download or read book Differential Equations with Operator Coefficients written by Vladimir Kozlov and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first systematic, self-contained presentation of a theory of arbitrary order ODEs with unbounded operator coefficients in a Hilbert or Banach space. Developed over the last 10 years by the authors, it deals with conditions of solvability, classes of uniqueness, estimates for solutions and asymptotic representations of solutions at infinity.

Download or read book Semigroups of Linear Operators and Applications to Partial Differential Equations written by Amnon Pazy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become a necessary discipline in functional analysis and differential equations. This book presents that theory and its basic applications, and the last two chapters give a connected account of the applications to partial differential equations.

Download or read book Operator Functions And Operator Equations written by Michael Gil' and published by World Scientific. This book was released on 2017-09-08 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to norm estimates for operator-valued functions of one and two operator arguments, as well as to their applications to spectrum perturbations of operators and to linear operator equations, i.e. to equations whose solutions are linear operators. Linear operator equations arise in both mathematical theory and engineering practice. The norm estimates suggested in the book have applications to the theories of ordinary differential, difference, functional-differential and integro-differential equations, as well as to the theories of integral operators and analytic functions. This book provides new tools for specialists in matrix theory and functional analysis. A significant part of the book covers the theory of triangular representations of operators that was developed by L de Branges, M S Brodskii, I C Gohberg, M G Krein, M S Livsic and other mathematicians.

Download or read book Functional Equations with Causal Operators written by C. Corduneanu and published by CRC Press. This book was released on 2002-09-05 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with cau

Download or read book Methods for Solving Operator Equations written by V. P. Tanana and published by Walter de Gruyter. This book was released on 2012-02-13 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

Download or read book Linear Operator Equations written by M. Thamban Nair and published by World Scientific. This book was released on 2009 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not often be possible or may not be worth looking for due to physical constraints. In such situations, it is desirable to know how the so-called approximate solution approximates the exact solution, and what the error involved in such procedures would be. This book is concerned with the investigation of the above theoretical issues related to approximately solving linear operator equations. The main tools used for this purpose are basic results from functional analysis and some rudimentary ideas from numerical analysis. To make this book more accessible to readers, no in-depth knowledge on these disciplines is assumed for reading this book.

Download or read book Perturbation theory for linear operators written by Tosio Kato and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Operator Theory and Differential Equations written by Anatoly G. Kusraev and published by Springer Nature. This book was released on 2021-01-13 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume features selected papers from The Fifteenth International Conference on Order Analysis and Related Problems of Mathematical Modeling, which was held in Vladikavkaz, Russia, on 15 - 20th July 2019. Intended for mathematicians specializing in operator theory, functional spaces, differential equations or mathematical modeling, the book provides a state-of-the-art account of various fascinating areas of operator theory, ranging from various classes of operators (positive operators, convolution operators, backward shift operators, singular and fractional integral operators, partial differential operators) to important applications in differential equations, inverse problems, approximation theory, metric theory of surfaces, the Hubbard model, social stratification models, and viscid incompressible fluids.

Download or read book Pseudo Differential Operators Complex Analysis and Partial Differential Equations written by Bert-Wolfgang Schulze and published by Springer Science & Business Media. This book was released on 2010-03-01 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consists of the expository paper based on the 6-hour minicourse given by Professor Bert-Wolfgang Schulze, and sixteen papers based on lectures given at the workshop and on invitations.