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Author: D.A. Klyushin Publisher: Springer Science & Business Media ISBN: 1461406196 Category : Mathematics Languages : en Pages : 219
Book Description
Abstract models for many problems in science and engineering take the form of an operator equation. The resolution of these problems often requires determining the existence and uniqueness of solutions to these equations. "Generalized Solutions of Operator Equations and Extreme Elements" presents recently obtained results in the study of the generalized solutions of operator equations and extreme elements in linear topological spaces. The presented results offer new methods of identifying these solutions and studying their properties. These new methods involve the application of a priori estimations and a general topological approach to construct generalized solutions of linear and nonlinear operator equations. The monograph is intended for mathematicians, graduate students and researchers studying functional analysis, operator theory, and the theory of optimal control.
Author: D.A. Klyushin Publisher: Springer Science & Business Media ISBN: 1461406196 Category : Mathematics Languages : en Pages : 219
Book Description
Abstract models for many problems in science and engineering take the form of an operator equation. The resolution of these problems often requires determining the existence and uniqueness of solutions to these equations. "Generalized Solutions of Operator Equations and Extreme Elements" presents recently obtained results in the study of the generalized solutions of operator equations and extreme elements in linear topological spaces. The presented results offer new methods of identifying these solutions and studying their properties. These new methods involve the application of a priori estimations and a general topological approach to construct generalized solutions of linear and nonlinear operator equations. The monograph is intended for mathematicians, graduate students and researchers studying functional analysis, operator theory, and the theory of optimal control.
Author: Ronghua Li Publisher: CRC Press ISBN: 1482270218 Category : Mathematics Languages : en Pages : 472
Book Description
This text presents a comprehensive mathematical theory for elliptic, parabolic, and hyperbolic differential equations. It compares finite element and finite difference methods and illustrates applications of generalized difference methods to elastic bodies, electromagnetic fields, underground water pollution, and coupled sound-heat flows.
Author: Vitalij P. Tanana Publisher: VSP ISBN: 9789067642378 Category : Mathematics Languages : en Pages : 236
Book Description
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.
Author: Mohammad Sal Moslehian Publisher: Springer Nature ISBN: 3031253868 Category : Mathematics Languages : en Pages : 763
Book Description
This book concerns matrix and operator equations that are widely applied in various disciplines of science to formulate challenging problems and solve them in a faithful way. The main aim of this contributed book is to study several important matrix and operator equalities and equations in a systematic and self-contained fashion. Some powerful methods have been used to investigate some significant equations in functional analysis, operator theory, matrix analysis, and numerous subjects in the last decades. The book is divided into two parts: (I) Matrix Equations and (II) Operator Equations. In the first part, the state-of-the-art of systems of matrix equations is given and generalized inverses are used to find their solutions. The semi-tensor product of matrices is used to solve quaternion matrix equations. The contents of some chapters are related to the relationship between matrix inequalities, matrix means, numerical range, and matrix equations. In addition, quaternion algebras and their applications are employed in solving some famous matrix equations like Sylvester, Stein, and Lyapunov equations. A chapter devoted to studying Hermitian polynomial matrix equations, which frequently arise from linear-quadratic control problems. Moreover, some classical and recently discovered inequalities for matrix exponentials are reviewed. In the second part, the latest developments in solving several equations appearing in modern operator theory are demonstrated. These are of interest to a wide audience of pure and applied mathematicians. For example, the Daugavet equation in the linear and nonlinear setting, iterative processes and Volterra-Fredholm integral equations, semicircular elements induced by connected finite graphs, free probability, singular integral operators with shifts, and operator differential equations closely related to the properties of the coefficient operators in some equations are discussed. The chapters give a comprehensive account of their subjects. The exhibited chapters are written in a reader-friendly style and can be read independently. Each chapter contains a rich bibliography. This book is intended for use by both researchers and graduate students of mathematics, physics, and engineering.
Author: Ioan I Vrabie Publisher: World Scientific Publishing Company ISBN: 981474980X Category : Mathematics Languages : en Pages : 529
Book Description
This book presents, in a unitary frame and from a new perspective, the main concepts and results of one of the most fascinating branches of modern mathematics, namely differential equations, and offers the reader another point of view concerning a possible way to approach the problems of existence, uniqueness, approximation, and continuation of the solutions to a Cauchy problem. In addition, it contains simple introductions to some topics which are not usually included in classical textbooks: the exponential formula, conservation laws, generalized solutions, Caratheodory solutions, differential inclusions, variational inequalities, viability, invariance, and gradient systems.In this new edition, some typos have been corrected and two new topics have been added: Delay differential equations and differential equations subjected to nonlocal initial conditions. The bibliography has also been updated and expanded.
Author: Yanfei Wang Publisher: Springer Science & Business Media ISBN: 3642137423 Category : Mathematics Languages : en Pages : 354
Book Description
"Optimization and Regularization for Computational Inverse Problems and Applications" focuses on advances in inversion theory and recent developments with practical applications, particularly emphasizing the combination of optimization and regularization for solving inverse problems. This book covers both the methods, including standard regularization theory, Fejer processes for linear and nonlinear problems, the balancing principle, extrapolated regularization, nonstandard regularization, nonlinear gradient method, the nonmonotone gradient method, subspace method and Lie group method; and the practical applications, such as the reconstruction problem for inverse scattering, molecular spectra data processing, quantitative remote sensing inversion, seismic inversion using the Lie group method, and the gravitational lensing problem. Scientists, researchers and engineers, as well as graduate students engaged in applied mathematics, engineering, geophysics, medical science, image processing, remote sensing and atmospheric science will benefit from this book. Dr. Yanfei Wang is a Professor at the Institute of Geology and Geophysics, Chinese Academy of Sciences, China. Dr. Sc. Anatoly G. Yagola is a Professor and Assistant Dean of the Physical Faculty, Lomonosov Moscow State University, Russia. Dr. Changchun Yang is a Professor and Vice Director of the Institute of Geology and Geophysics, Chinese Academy of Sciences, China.
Author: D.A. Klyushin
Author: D.A. Klyushin
Author: Ronghua Li
Author: Vitalij P. Tanana
Author: George Dincă
Author: Mark Aleksandrovich Krasnoselʹskiĭ
Author: Mohammad Sal Moslehian
Author: Andrew Maxwell Olson
Author: 
Author: Ioan I Vrabie
Author: Yanfei Wang