Generalized Inverses Theory And Computations
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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.
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.
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.
Algebraic Theory Of Generalized Inverses
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Author : Jianlong Chen
language : en
Publisher: Springer Nature
Release Date :
Algebraic Theory Of Generalized Inverses written by Jianlong Chen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
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.
Elements Of The Theory Of Generalized Inverses For Matrices
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Author : Randall E. Cline
language : en
Publisher:
Release Date : 1979
Elements Of The Theory Of Generalized Inverses For Matrices written by Randall E. Cline and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Linear operators categories.
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 And Applications
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Author : M. Zuhair Nashed
language : en
Publisher: Elsevier
Release Date : 2014-05-10
Generalized Inverses And Applications written by M. Zuhair Nashed and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
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.
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.
Recent Applications Of Generalized Inverses
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Author : Stephen La Vern Campbell
language : en
Publisher: Pitman Advanced Publishing Program
Release Date : 1982
Recent Applications Of Generalized Inverses written by Stephen La Vern Campbell and has been published by Pitman Advanced Publishing Program this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
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.