Recent Applications Of Generalized Inverses

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Generalized Inverses

Ivan Kyrchei
Generalized Inverses Book PDF

Author : Ivan Kyrchei
Publisher : Nova Science Publishers
Page : 288 pages
File Size : 47,6 Mb
Release : 2022
Category : Mathematics
ISBN : 1685075134

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Generalized Inverses by Ivan Kyrchei Pdf

"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"--

Generalized Inverses

Adi Ben-Israel,Thomas N.E. Greville
Generalized Inverses Book PDF

Author : Adi Ben-Israel,Thomas N.E. Greville
Publisher : Springer Science & Business Media
Page : 420 pages
File Size : 45,8 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387216348

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Generalized Inverses by Adi Ben-Israel,Thomas N.E. Greville Pdf

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.

Recent Applications of Generalized Inverses

Stephen La Vern Campbell
Recent Applications of Generalized Inverses Book PDF

Author : Stephen La Vern Campbell
Publisher : Pitman Advanced Publishing Program
Page : 292 pages
File Size : 41,7 Mb
Release : 1982
Category : Mathematics
ISBN : UCAL:B4509778

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Recent Applications of Generalized Inverses by Stephen La Vern Campbell Pdf

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.

Generalized Inverses and Applications

M. Zuhair Nashed
Generalized Inverses and Applications Book PDF

Author : M. Zuhair Nashed
Publisher : Elsevier
Page : 1069 pages
File Size : 43,9 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483270296

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Generalized Inverses and Applications by M. Zuhair Nashed Pdf

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.

Generalized Inverses of Linear Transformations

Stephen L. Campbell,Carl D. Meyer
Generalized Inverses of Linear Transformations Book PDF

Author : Stephen L. Campbell,Carl D. Meyer
Publisher : SIAM
Page : 289 pages
File Size : 49,8 Mb
Release : 2009-01-01
Category : Mathematics
ISBN : 9780898719048

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Generalized Inverses of Linear Transformations by Stephen L. Campbell,Carl D. Meyer Pdf

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.

Generalized Inverses: Theory and Computations

Guorong Wang,Yimin Wei,Sanzheng Qiao
Generalized Inverses Theory and Computations Book PDF

Author : Guorong Wang,Yimin Wei,Sanzheng Qiao
Publisher : Springer
Page : 378 pages
File Size : 50,7 Mb
Release : 2018-05-12
Category : Mathematics
ISBN : 9789811301469

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Generalized Inverses: Theory and Computations by Guorong Wang,Yimin Wei,Sanzheng Qiao Pdf

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.

Computation of Generalized Matrix Inverses and Applications

Ivan Stanimirović
Computation of Generalized Matrix Inverses and Applications Book PDF

Author : Ivan Stanimirović
Publisher : CRC Press
Page : 199 pages
File Size : 45,9 Mb
Release : 2017-12-14
Category : Mathematics
ISBN : 9781351630054

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Computation of Generalized Matrix Inverses and Applications by Ivan Stanimirović Pdf

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 Inverse of Matrices and Its Applications

Calyampudi Radhakrishna Rao,Sujit Kumar Mitra
Generalized Inverse of Matrices and Its Applications Book PDF

Author : Calyampudi Radhakrishna Rao,Sujit Kumar Mitra
Publisher : John Wiley & Sons
Page : 264 pages
File Size : 51,8 Mb
Release : 1971
Category : Mathematics
ISBN : MINN:31951000012834C

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Generalized Inverse of Matrices and Its Applications by Calyampudi Radhakrishna Rao,Sujit Kumar Mitra Pdf

Notations and preliminaries; Generalized inverse of a matrix; Three basic types of g-inverses; Other special types of g-inverse; Projectors, idempotent matrices and partial isometry; Simulatneous reduction of a pair of herminitian forms; Estimation of parameters in linear models; Conditions for optimality and validity of least-squares theory; Distribution of quadratic forms; Miscellaneous applications of g-inverses; Computational methods; Bibliography on generalized inverses and applications; Index.

Theory of Generalized Inverses Over Commutative Rings

K.P.S. Bhaskara Rao
Theory of Generalized Inverses Over Commutative Rings Book PDF

Author : K.P.S. Bhaskara Rao
Publisher : CRC Press
Page : 192 pages
File Size : 40,9 Mb
Release : 2002-03-21
Category : Mathematics
ISBN : 9780203218877

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Theory of Generalized Inverses Over Commutative Rings by K.P.S. Bhaskara Rao Pdf

The theory of generalized inverses of real or complex matrices has been expertly developed and documented. But the generalized inverses of matrices over rings have received comprehensive treatment only recently. In this book, the author, who contributed to the research and development of the theory, explains his results. He explores regular element

Generalized Inverses: Algorithms and Applications

Ivan Kyrchei
Generalized Inverses Algorithms and Applications Book PDF

Author : Ivan Kyrchei
Publisher : Unknown
Page : 128 pages
File Size : 46,6 Mb
Release : 2021-12-31
Category : Electronic
ISBN : 1685073565

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Generalized Inverses: Algorithms and Applications by Ivan Kyrchei Pdf

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.

Matrix Partial Orders, Shorted Operators and Applications

Sujit Kumar Mitra,P. Bhimasankaram,Saroj B. Malik
Matrix Partial Orders Shorted Operators and Applications Book PDF

Author : Sujit Kumar Mitra,P. Bhimasankaram,Saroj B. Malik
Publisher : World Scientific
Page : 463 pages
File Size : 44,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9789812838452

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Matrix Partial Orders, Shorted Operators and Applications by Sujit Kumar Mitra,P. Bhimasankaram,Saroj B. Malik Pdf

1. Introduction. 1.1. Matrix orders. 1.2. Parallel sum and shorted operator. 1.3. A tour through the rest of the monograph -- 2. Matrix decompositions and generalized inverses. 2.1. Introduction. 2.2. Matrix decompositions. 2.3. Generalized inverse of a matrix. 2.4. The group inverse. 2.5. Moore-Penrose inverse. 2.6. Generalized inverses of modified matrices. 2.7. Simultaneous diagonalization. 2.8. Exercises -- 3. The minus order. 3.1. Introduction. 3.2. Space pre-order. 3.3. Minus order - some characterizations. 3.4. Matrices above/below a given matrix under the minus order. 3.5. Subclass of g-inverses A[symbol] of A such that [symbol]A = A[symbol]B and AA[symbol]=BA[symbol] when A

Optimization and Design of Geodetic Networks

Erik W. Grafarend,Fernando Sansò
Optimization and Design of Geodetic Networks Book PDF

Author : Erik W. Grafarend,Fernando Sansò
Publisher : Springer Science & Business Media
Page : 621 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642706592

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Optimization and Design of Geodetic Networks by Erik W. Grafarend,Fernando Sansò Pdf

During the period April 25th to May 10th, 1984 the 3rd Course of the International School of Advanced Geodesy entitled "Optimization and Design of Geodetic Networks" took place in Erice. The main subject of the course is clear from the title and consisted mainly of that particular branch of network analysis, which results from applying general concepts of mathematical optimization to the design of geodetic networks. As al ways when dealing with optimization problems, there is an a-priori choice of the risk (or gain) function which should be minimized (or maximized) according to the specific interest of the "designer", which might be either of a scientific or of an economic nature or even of both. These aspects have been reviewed in an intro ductory lecture in which the particular needs arising in a geodetic context and their analytical representations are examined. Subsequently the main body of the optimization problem, which has been conven tionally divided into zero, first, second and third order design problems, is presented. The zero order design deals with the estimability problem, in other words with the definition of which parameters are estimable from a given set of observa tions. The problem results from the fact that coordinates of points are not univocally determined from the observations of relative quantities such as angles and distances, whence a problem of the optimal choice of a reference system, the so-called "datum problem" arises.

Numerical And Symbolic Computations Of Generalized Inverses

Yimin Wei,Predrag Stanimirovic,Marko Petkovic
Numerical And Symbolic Computations Of Generalized Inverses Book PDF

Author : Yimin Wei,Predrag Stanimirovic,Marko Petkovic
Publisher : World Scientific
Page : 472 pages
File Size : 54,6 Mb
Release : 2018-07-18
Category : Mathematics
ISBN : 9789813238688

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Numerical And Symbolic Computations Of Generalized Inverses by Yimin Wei,Predrag Stanimirovic,Marko Petkovic Pdf

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.

Infinite Matrices and Their Recent Applications

P.N. Shivakumar,K.C. Sivakumar,Yang Zhang
Infinite Matrices and Their Recent Applications Book PDF

Author : P.N. Shivakumar,K.C. Sivakumar,Yang Zhang
Publisher : Springer
Page : 118 pages
File Size : 41,7 Mb
Release : 2016-06-20
Category : Mathematics
ISBN : 9783319301808

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Infinite Matrices and Their Recent Applications by P.N. Shivakumar,K.C. Sivakumar,Yang Zhang Pdf

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.

Extremal Methods and Systems Analysis

A. V. Fiacco,K. O. Kortanek
Extremal Methods and Systems Analysis Book PDF

Author : A. V. Fiacco,K. O. Kortanek
Publisher : Springer Science & Business Media
Page : 554 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642464140

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Extremal Methods and Systems Analysis by A. V. Fiacco,K. O. Kortanek Pdf

The papers appearing in this Volume were selected from a collec tion of papers presented at the Internationa~ Symposium on Extrema~ Methods and Systems Ana~ysis on the Occasion of Professor A. Charnes' 60th Birthday, at the University of Texas in Austin, 13-15 September 1977. As coeditors, we have followed the normal editorial procedures of scholarly journals. We have obtained invaluable assistance from a number of colleagues who essentially performed the duties of associate editors, coordinating most of the reviews. All papers except those appearing in the Historica~ Perspectives section were refereed by at least two individuals with competency in the respective area. Because of the wide range and diversity of the topics, it would have been im possible for us to make a consistently rational selection of papers without the help of the associate editors and referees. We are indeed grateful to them. The breadth of extremal methods and systems analysis, suggested by the range of topics covered in these papers, is characteristic of the field and also of the scholarly work of Professor Charnes. Extre mal methods and systems analysis has been a pioneering and systematic approach to the development and application of new scientific theories and methods for problems of management and operations in both the pri vate and public sectors, spanning all major disciplines from economics to engineering.