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Numerical And Symbolic Computations Of Generalized Inverses
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Book Synopsis Numerical And Symbolic Computations Of Generalized Inverses by : Yimin Wei
Download or read book Numerical And Symbolic Computations Of Generalized Inverses written by Yimin Wei and published by World Scientific. This book was released on 2018-07-18 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce new methods connecting numerics and symbolic computations, i.e., both the direct and iterative methods as well as the symbolic method for computing the generalized inverses. These will be useful for Engineers and Statisticians, in addition to applied mathematicians.Also, main applications of generalized inverses will be presented. Symbolic method covered in our book but not discussed in other book, which is important for numerical-symbolic computations.
Book Synopsis Numerical and Symbolic Computations of Generalized Inverses by : Yimin Wei (Mathematics professor)
Download or read book Numerical and Symbolic Computations of Generalized Inverses written by Yimin Wei (Mathematics professor) and published by . This book was released on 2001 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Generalized Inverses: Theory and Computations by : Guorong Wang
Download or read book Generalized Inverses: Theory and Computations written by Guorong Wang and published by Springer. This book was released on 2018-05-12 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book begins with the fundamentals of the generalized inverses, then moves to more advanced topics. It presents a theoretical study of the generalization of Cramer's rule, determinant representations of the generalized inverses, reverse order law of the generalized inverses of a matrix product, structures of the generalized inverses of structured matrices, parallel computation of the generalized inverses, perturbation analysis of the generalized inverses, an algorithmic study of the computational methods for the full-rank factorization of a generalized inverse, generalized singular value decomposition, imbedding method, finite method, generalized inverses of polynomial matrices, and generalized inverses of linear operators. This book is intended for researchers, postdocs, and graduate students in the area of the generalized inverses with an undergraduate-level understanding of linear algebra.
Book Synopsis Generalized Inverses by : Adi Ben-Israel
Download or read book Generalized Inverses written by Adi Ben-Israel and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition accounts for many major developments in generalized inverses while maintaining the informal and leisurely style of the 1974 first edition. Added material includes a chapter on applications, new exercises, and an appendix on the work of E.H. Moore.
Book Synopsis Computation of Generalized Matrix Inverses and Applications by : Ivan Stanimirović
Download or read book Computation of Generalized Matrix Inverses and Applications written by Ivan Stanimirović and published by CRC Press. This book was released on 2017-12-14 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers a gradual exposition to matrix theory as a subject of linear algebra. It presents both the theoretical results in generalized matrix inverses and the applications. The book is as self-contained as possible, assuming no prior knowledge of matrix theory and linear algebra. The book first addresses the basic definitions and concepts of an arbitrary generalized matrix inverse with special reference to the calculation of {i,j,...,k} inverse and the Moore–Penrose inverse. Then, the results of LDL* decomposition of the full rank polynomial matrix are introduced, along with numerical examples. Methods for calculating the Moore–Penrose’s inverse of rational matrix are presented, which are based on LDL* and QDR decompositions of the matrix. A method for calculating the A(2)T;S inverse using LDL* decomposition using methods is derived as well as the symbolic calculation of A(2)T;S inverses using QDR factorization. The text then offers several ways on how the introduced theoretical concepts can be applied in restoring blurred images and linear regression methods, along with the well-known application in linear systems. The book also explains how the computation of generalized inverses of matrices with constant values is performed. It covers several methods, such as methods based on full-rank factorization, Leverrier–Faddeev method, method of Zhukovski, and variations of the partitioning method.
Book Synopsis Generalized Inverses of Linear Transformations by : Stephen L. Campbell
Download or read book Generalized Inverses of Linear Transformations written by Stephen L. Campbell and published by SIAM. This book was released on 2009-01-01 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized (or pseudo-) inverse concepts routinely appear throughout applied mathematics and engineering, in both research literature and textbooks. Although the basic properties are readily available, some of the more subtle aspects and difficult details of the subject are not well documented or understood. First published in 1979, Generalized Inverses of Linear Transformations remains up-to-date and readable, and it includes chapters on Markov chains and the Drazin inverse methods that have become significant to many problems in applied mathematics. The book provides comprehensive coverage of the mathematical theory of generalized inverses coupled with a wide range of important and practical applications that includes topics in electrical and computer engineering, control and optimization, computing and numerical analysis, statistical estimation, and stochastic processes. Audience: intended for use as a reference by applied scientists and engineers.
Book Synopsis Matrix and Operator Equations and Applications by : Mohammad Sal Moslehian
Download or read book Matrix and Operator Equations and Applications written by Mohammad Sal Moslehian and published by Springer Nature. This book was released on 2023-07-29 with total page 763 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebraic Informatics by : Miroslav Ćirić
Download or read book Algebraic Informatics written by Miroslav Ćirić and published by Springer. This book was released on 2019-06-17 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 8th International Conference on Algebraic Informatics, CAI 2019, held in Niš, Serbia, in June/July 2019. The 20 revised papers presented were carefully reviewed and selected from 35 submissions. The papers present research at the intersection of theoretical computer science, algebra, and related areas. They report original unpublished research and cover a broad range of topics from automata theory and logic, cryptography and coding theory, computer algebra, design theory, natural and quantum computation, and related areas.
Book Synopsis Numerical and Symbolic Scientific Computing by : Ulrich Langer
Download or read book Numerical and Symbolic Scientific Computing written by Ulrich Langer and published by Springer Science & Business Media. This book was released on 2011-11-19 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the state of the art and results and also includes articles pointing to future developments. Most of the articles center around the theme of linear partial differential equations. Major aspects are fast solvers in elastoplasticity, symbolic analysis for boundary problems, symbolic treatment of operators, computer algebra, and finite element methods, a symbolic approach to finite difference schemes, cylindrical algebraic decomposition and local Fourier analysis, and white noise analysis for stochastic partial differential equations. Further numerical-symbolic topics range from applied and computational geometry to computer algebra methods used for total variation energy minimization.
Book Synopsis Symbolic and Numerical Scientific Computation by : Franz Winkler
Download or read book Symbolic and Numerical Scientific Computation written by Franz Winkler and published by Springer. This book was released on 2003-08-03 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: The thoroughly refereed post-proceedings of the Second International Conference on Symbolic and Numerical Scientific Computation, SNSC 2001, held in Hagenberg, Austria, in September 2001. The 19 revised full papers presented were carefully selected during two rounds of reviewing and improvement. The papers are organized in topical sections on symbolics and numerics of differential equations, symbolics and numerics in algebra and geometry, and applications in physics and engineering.
Book Synopsis Algebraic Properties of Generalized Inverses by : Dragana S. Cvetković‐Ilić
Download or read book Algebraic Properties of Generalized Inverses written by Dragana S. Cvetković‐Ilić and published by Springer. This book was released on 2017-10-07 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses selected topics in the theory of generalized inverses. Following a discussion of the “reverse order law” problem and certain problems involving completions of operator matrices, it subsequently presents a specific approach to solving the problem of the reverse order law for {1} -generalized inverses. Particular emphasis is placed on the existence of Drazin invertible completions of an upper triangular operator matrix; on the invertibility and different types of generalized invertibility of a linear combination of operators on Hilbert spaces and Banach algebra elements; on the problem of finding representations of the Drazin inverse of a 2x2 block matrix; and on selected additive results and algebraic properties for the Drazin inverse. In addition to the clarity of its content, the book discusses the relevant open problems for each topic discussed. Comments on the latest references on generalized inverses are also included. Accordingly, the book will be useful for graduate students, PhD students and researchers, but also for a broader readership interested in these topics.
Book Synopsis Generalized Inverses and Applications by : M. Zuhair Nashed
Download or read book Generalized Inverses and Applications written by M. Zuhair Nashed and published by Elsevier. This book was released on 2014-05-10 with total page 1069 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Inverses and Applications, contains the proceedings of an Advanced Seminar on Generalized Inverses and Applications held at the University of Wisconsin-Madison on October 8-10, 1973 under the auspices of the university's Mathematics Research Center. The seminar provided a forum for discussing the basic theory of generalized inverses and their applications to analysis and operator equations. Numerical analysis and approximation methods are considered, along with applications to statistics and econometrics, optimization, system theory, and operations research. Comprised of 14 chapters, this book begins by describing a unified approach to generalized inverses of linear operators, with particular reference to algebraic, topological, extremal, and proximinal properties. The reader is then introduced to the algebraic aspects of the generalized inverse of a rectangular matrix; the Fredholm pseudoinverse; and perturbations and approximations for generalized inverses and linear operator equations. Subsequent chapters deal with various applications of generalized inverses, including programming, games, and networks, as well as estimation and aggregation in econometrics. This monograph will be of interest to mathematicians and students of mathematics.
Book Synopsis Algebraic Theory of Generalized Inverses by : Jianlong Chen
Download or read book Algebraic Theory of Generalized Inverses written by Jianlong Chen and published by Springer Nature. This book was released on with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Infinite Matrices and Their Recent Applications by : P.N. Shivakumar
Download or read book Infinite Matrices and Their Recent Applications written by P.N. Shivakumar and published by Springer. This book was released on 2016-06-20 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph covers the theory of finite and infinite matrices over the fields of real numbers, complex numbers and over quaternions. Emphasizing topics such as sections or truncations and their relationship to the linear operator theory on certain specific separable and sequence spaces, the authors explore techniques like conformal mapping, iterations and truncations that are used to derive precise estimates in some cases and explicit lower and upper bounds for solutions in the other cases. Most of the matrices considered in this monograph have typically special structures like being diagonally dominated or tridiagonal, possess certain sign distributions and are frequently nonsingular. Such matrices arise, for instance, from solution methods for elliptic partial differential equations. The authors focus on both theoretical and computational aspects concerning infinite linear algebraic equations, differential systems and infinite linear programming, among others. Additionally, the authors cover topics such as Bessel’s and Mathieu’s equations, viscous fluid flow in doubly connected regions, digital circuit dynamics and eigenvalues of the Laplacian.
Book Synopsis Generalized Inverses by : Ivan Kyrchei
Download or read book Generalized Inverses written by Ivan Kyrchei and published by Nova Science Publishers. This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Generalized Inverses: Algorithms and Applications demonstrates some of the latest hot topics on generalized inverse matrices and their applications. Each article has been carefully selected to present substantial research results. Topics discussed herein include recent advances in exploring of generalizations of the core inverse, particularly in composing appropriate outer inverses and the Moore-Penrose inverse such as OMP, MPO and MPOMP inverses; in analyzing of properties of the BT inverse and the BT-order; in perturbation estimations for the Drazin inverse; in using generalized inverses to solve systems of quaternion matrix equations and Sylvester-type tensor equations under t-product; in computing and approximating the matrix generalized inverses by hyperpower family of iterative methods of arbitrary convergence order; and in studying of the weighted pseudoinverse matrices with singular indefinite weights"--
Book Synopsis Recent Applications of Generalized Inverses by : Stephen La Vern Campbell
Download or read book Recent Applications of Generalized Inverses written by Stephen La Vern Campbell and published by Pitman Advanced Publishing Program. This book was released on 1982 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of original papers shows the variety of current research into generalized inverses of linear transformations and their applications. The papers are grouped in sections, covering topics which include systems theory, operator theory, numerical methods, applications to Markov chains, and interpolation theory.
Book Synopsis Handbook of Linear Algebra by : Leslie Hogben
Download or read book Handbook of Linear Algebra written by Leslie Hogben and published by CRC Press. This book was released on 2013-11-26 with total page 1906 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and
