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Approximate Solution Of Linear Operator Equations
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Book Synopsis Approximate Solution of Operator Equations by : M.A. Krasnosel'skii
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.
Book Synopsis Linear Operator Equations by : M. Thamban Nair
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.
Book Synopsis Approximate Solutions of Operator Equations by : Mingjun Chen
Download or read book Approximate Solutions of Operator Equations written by Mingjun Chen and published by World Scientific. This book was released on 1997 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an elementary and self-contained introduction to many fundamental issues concerning approximate solutions of operator equations formulated in an abstract Banach space setting, including important topics such as solvability, computational schemes, convergence, stability and error estimates. The operator equations under investigation include various linear and nonlinear types of ordinary and partial differential equations, integral equations, and abstract evolution equations, which are frequently involved in applied mathematics and engineering applications.Each chapter contains well-selected examples and exercises, for the purposes of demonstrating the fundamental theories and methods developed in the text and familiarizing the reader with functional analysis techniques useful for numerical solutions of various operator equations.
Book Synopsis Approximate Solutions Of Operator Equations by : Guanrong Chen
Download or read book Approximate Solutions Of Operator Equations written by Guanrong Chen and published by World Scientific. This book was released on 1997-07-01 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an elementary and self-contained introduction to many fundamental issues concerning approximate solutions of operator equations formulated in an abstract Banach space setting, including important topics such as solvability, computational schemes, convergence, stability and error estimates. The operator equations under investigation include various linear and nonlinear types of ordinary and partial differential equations, integral equations, and abstract evolution equations, which are frequently involved in applied mathematics and engineering applications.Each chapter contains well-selected examples and exercises, for the purposes of demonstrating the fundamental theories and methods developed in the text and familiarizing the reader with functional analysis techniques useful for numerical solutions of various operator equations.
Book Synopsis Approximate Solution of Operator Equations with Applications by : Ioannis K. Argyros
Download or read book Approximate Solution of Operator Equations with Applications written by Ioannis K. Argyros and published by World Scientific. This book was released on 2005 with total page 530 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.
Book Synopsis Approximate Solution of Linear Operator Equations by : M. Thamban Nair
Download or read book Approximate Solution of Linear Operator Equations written by M. Thamban Nair and published by . This book was released on 1998 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Approximate Solution Of Operator Equations With Applications by : Ioannis K Argyros
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.
Book Synopsis On the Optimal Approximate Solution of Linear Operator Equations with Inadequate Data by : Tze-san David Lee
Download or read book On the Optimal Approximate Solution of Linear Operator Equations with Inadequate Data written by Tze-san David Lee and published by . This book was released on 1976 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Iterative Methods for the Solution of a Linear Operator Equation in Hilbert Space by : W.M., III. Patterson
Download or read book Iterative Methods for the Solution of a Linear Operator Equation in Hilbert Space written by W.M., III. Patterson and published by Springer. This book was released on 2006-11-15 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this expository work we shall conduct a survey of iterative techniques for solving the linear operator equations Ax=y in a Hilbert space. Whenever convenient these iterative schemes are given in the context of a complex Hilbert space -- Chapter II is devoted to those methods (three in all) which are given only for real Hilbert space. Thus chapter III covers those methods which are valid in a complex Hilbert space except for the two methods which are singled out for special attention in the last two chapters. Specifically, the method of successive approximations is covered in Chapter IV, and Chapter V consists of a discussion of gradient methods. While examining these techniques, our primary concern will be with the convergence of the sequence of approximate solutions. However, we shall often look at estimates of the error and the speed of convergence of a method.
Book Synopsis A Class of Approximate Solutions to Linear Operator Equations by : Grace Wahba
Download or read book A Class of Approximate Solutions to Linear Operator Equations written by Grace Wahba and published by . This book was released on 1971 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Approximate Solution of Operator Equations by : Mark Aleksandrovich Krasnoselʹskiĭ
Download or read book Approximate Solution of Operator Equations written by Mark Aleksandrovich Krasnoselʹskiĭ and published by . This book was released on 1969 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Approximate Solution of Random Equations by : Albert T. Bharucha-Reid
Download or read book Approximate Solution of Random Equations written by Albert T. Bharucha-Reid and published by North-Holland. This book was released on 1979 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Iterative Methods for the Solution of a Linear Operator Equation in Hilbert Space by : Walter Mead Patterson
Download or read book Iterative Methods for the Solution of a Linear Operator Equation in Hilbert Space written by Walter Mead Patterson and published by Lecture Notes in Mathematics. This book was released on 1974-07-22 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this expository work we shall conduct a survey of iterative techniques for solving the linear operator equations Ax=y in a Hilbert space. Whenever convenient these iterative schemes are given in the context of a complex Hilbert space -- Chapter II is devoted to those methods (three in all) which are given only for real Hilbert space. Thus chapter III covers those methods which are valid in a complex Hilbert space except for the two methods which are singled out for special attention in the last two chapters. Specifically, the method of successive approximations is covered in Chapter IV, and Chapter V consists of a discussion of gradient methods. While examining these techniques, our primary concern will be with the convergence of the sequence of approximate solutions. However, we shall often look at estimates of the error and the speed of convergence of a method.
Book Synopsis Practical Approximate Solutions to Linear Operator Equations when the Data are Noisy by : Grace Wahba
Download or read book Practical Approximate Solutions to Linear Operator Equations when the Data are Noisy written by Grace Wahba and published by . This book was released on 1975 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Spectral Approximation of Linear Operators by : Francoise Chatelin
Download or read book Spectral Approximation of Linear Operators written by Francoise Chatelin and published by SIAM. This book was released on 2011-05-26 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: New York: Academic Press, 1983.
Book Synopsis Methods for Solving Operator Equations by : V. P. Tanana
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.
Book Synopsis Polynomial Operator Equations in Abstract Spaces and Applications by : Ioannis K. Argyros
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 2020-10-07 with total page 586 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 equation
