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Computation Of Generalized Matrix Inverses And Applications

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Computation Of Generalized Matrix Inverses And Applications

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Author : Ivan Stanimirović
language : en
Publisher: CRC Press
Release Date : 2017-12-14

Computation Of Generalized Matrix Inverses And Applications written by Ivan Stanimirović and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-14 with Mathematics categories.

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.

Generalized Inverses

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Author : Adi Ben-Israel
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18

Generalized Inverses written by Adi Ben-Israel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-18 with Mathematics categories.

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.

Generalized Inverses Of Linear Transformations

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Author : Stephen L. Campbell
language : en
Publisher: SIAM
Release Date : 2009-03-26

Generalized Inverses Of Linear Transformations written by Stephen L. Campbell and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-26 with Mathematics categories.

Provides comprehensive coverage of the mathematical theory of generalized inverses and a wide range of important and practical applications.

Computation Of Generalized Matrix Inverses And Applications

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Author : IVAN. STANIMIROVIC
language : en
Publisher: Apple Academic Press
Release Date : 2021-03-31

Computation Of Generalized Matrix Inverses And Applications written by IVAN. STANIMIROVIC and has been published by Apple Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-31 with Algebras, Linear categories.

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.

Generalized Inverses

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Author : Adi Ben-Israel
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-06-16

Numerical And Symbolic Computations Of Generalized Inverses

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Author : Yimin Wei
language : en
Publisher: World Scientific
Release Date : 2018-07-18

Numerical And Symbolic Computations Of Generalized Inverses written by Yimin Wei and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-18 with Mathematics categories.

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.

Generalized Inverses Theory And Computations

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Author : Guorong Wang
language : en
Publisher: Springer
Release Date : 2018-05-12

Generalized Inverses Theory And Computations written by Guorong Wang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-12 with Mathematics categories.

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.

Matrix Algebra

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Author : James E. Gentle
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-06

Matrix Algebra written by James E. Gentle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-06 with Mathematics categories.

Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. The first part of this book presents the relevant aspects of the theory of matrix algebra for applications in statistics. This part begins with the fundamental concepts of vectors and vector spaces, next covers the basic algebraic properties of matrices, then describes the analytic properties of vectors and matrices in the multivariate calculus, and finally discusses operations on matrices in solutions of linear systems and in eigenanalysis. This part is essentially self-contained. The second part of the book begins with a consideration of various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. The second part also describes some of the many applications of matrix theory in statistics, including linear models, multivariate analysis, and stochastic processes. The brief coverage in this part illustrates the matrix theory developed in the first part of the book. The first two parts of the book can be used as the text for a course in matrix algebra for statistics students, or as a supplementary text for various courses in linear models or multivariate statistics. The third part of this book covers numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Although the book is not tied to any particular software system, it describes and gives examples of the use of modern computer software for numerical linear algebra. This part is essentially self-contained, although it assumes some ability to program in Fortran or C and/or the ability to use R/S-Plus or Matlab. This part of the book can be used as the text for a course in statistical computing, or as a supplementary text for various courses that emphasize computations. The book includes a large number of exercises with some solutions provided in an appendix.

Advanced Intelligent Computing Theories And Applications

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Author : De-Shuang Huang
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-09

Advanced Intelligent Computing Theories And Applications written by De-Shuang Huang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-09 with Computers categories.

This volume, in conjunction with the two volumes CICS 0002 and LNCS 4681, constitutes the refereed proceedings of the Third International Conference on Intelligent Computing held in Qingdao, China, in August 2007. The 139 full papers published here were carefully reviewed and selected from among 2,875 submissions. These papers offer important findings and insights into the field of intelligent computing.

Matrix And Operator Equations And Applications

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Author : Mohammad Sal Moslehian
language : en
Publisher: Springer Nature
Release Date : 2023-07-29

Matrix And Operator Equations And Applications written by Mohammad Sal Moslehian and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-29 with Mathematics categories.

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.

Computation Of Generalized Matrix Inverses And Applications

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