Generalized Inverses Theory And Computations

Author : Guorong Wang,Yimin Wei,Sanzheng Qiao
Publisher : Springer
Page : 378 pages
File Size : 47,6 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.

Author : Adi Ben-Israel,Thomas N.E. Greville
Publisher : Springer Science & Business Media
Page : 420 pages
File Size : 48,9 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.

Author : Stephen L. Campbell,Carl D. Meyer
Publisher : SIAM
Page : 288 pages
File Size : 48,8 Mb
Release : 2009-03-26
Category : Mathematics
ISBN : 9780898716719

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

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

Author : Yimin Wei,Predrag Stanimirovic,Marko Petkovic
Publisher : World Scientific
Page : 472 pages
File Size : 46,8 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.

Author : Ivan Stanimirović
Publisher : CRC Press
Page : 280 pages
File Size : 55,9 Mb
Release : 2017-12-14
Category : Mathematics
ISBN : 9781351630061

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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.

Author : Randall E. Cline
Publisher : Unknown
Page : 104 pages
File Size : 49,8 Mb
Release : 1979
Category : Linear operators
ISBN : UOM:39015035721599

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Elements of the Theory of Generalized Inverses for Matrices by Randall E. Cline Pdf

Author : M. Zuhair Nashed
Publisher : Elsevier
Page : 1069 pages
File Size : 44,5 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.

Author : Ravindra B. Bapat,Steve J. Kirkland,K. Manjunatha Prasad,Simo Puntanen
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 40,5 Mb
Release : 2013-02-11
Category : Mathematics
ISBN : 9788132210535

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Combinatorial Matrix Theory and Generalized Inverses of Matrices by Ravindra B. Bapat,Steve J. Kirkland,K. Manjunatha Prasad,Simo Puntanen Pdf

This book consists of eighteen articles in the area of `Combinatorial Matrix Theory' and `Generalized Inverses of Matrices'. Original research and expository articles presented in this publication are written by leading Mathematicians and Statisticians working in these areas. The articles contained herein are on the following general topics: `matrices in graph theory', `generalized inverses of matrices', `matrix methods in statistics' and `magic squares'. In the area of matrices and graphs, speci_c topics addressed in this volume include energy of graphs, q-analog, immanants of matrices and graph realization of product of adjacency matrices. Topics in the book from `Matrix Methods in Statistics' are, for example, the analysis of BLUE via eigenvalues of covariance matrix, copulas, error orthogonal model, and orthogonal projectors in the linear regression models. Moore-Penrose inverse of perturbed operators, reverse order law in the case of inde_nite inner product space, approximation numbers, condition numbers, idempotent matrices, semiring of nonnegative matrices, regular matrices over incline and partial order of matrices are the topics addressed under the area of theory of generalized inverses. In addition to the above traditional topics and a report on CMTGIM 2012 as an appendix, we have an article on old magic squares from India.

Author : Mykhaylo Andriychuk
Publisher : BoD – Books on Demand
Page : 274 pages
File Size : 41,7 Mb
Release : 2023
Category : Mathematics
ISBN : 9781803558226

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Matrix Theory by Mykhaylo Andriychuk Pdf

Matrix Theory - Classics and Advances examines matrix theory and its application in solving a series of problems related to natural phenomena and applied science. It consists of eleven chapters divided into two sections. Section 1, "Theory and Progress", discusses the classical problems of matrix theory and its contribution to different fields of pure mathematics. Section 2, "Applications", contains the research related to the application of matrix theory in applied science.

Author : Juan R. Torregrosa,Alicia Cordero,Fazlollah Soleymani
Publisher : MDPI
Page : 494 pages
File Size : 54,5 Mb
Release : 2019-12-06
Category : Mathematics
ISBN : 9783039219407

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Iterative Methods for Solving Nonlinear Equations and Systems by Juan R. Torregrosa,Alicia Cordero,Fazlollah Soleymani Pdf

Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a non-trivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.

Author : R. T. Gregory,E. V. Krishnamurthy
Publisher : Springer Science & Business Media
Page : 204 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461252429

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Methods and Applications of Error-Free Computation by R. T. Gregory,E. V. Krishnamurthy Pdf

This book is written as an introduction to the theory of error-free computation. In addition, we include several chapters that illustrate how error-free com putation can be applied in practice. The book is intended for seniors and first year graduate students in fields of study involving scientific computation using digital computers, and for researchers (in those same fields) who wish to obtain an introduction to the subject. We are motivated by the fact that there are large classes of ill-conditioned problems, and there are numerically unstable algorithms, and in either or both of these situations we cannot tolerate rounding errors during the numerical computations involved in obtaining solutions to the problems. Thus, it is important to study finite number systems for digital computers which have the property that computation can be performed free of rounding errors. In Chapter I we discuss single-modulus and multiple-modulus residue number systems and arithmetic in these systems, where the operands may be either integers or rational numbers. In Chapter II we discuss finite-segment p-adic number systems and their relationship to the p-adic numbers of Hensel [1908]. Each rational number in a certain finite set is assigned a unique Hensel code and arithmetic operations using Hensel codes as operands is mathe matically equivalent to those same arithmetic operations using the cor responding rational numbers as operands. Finite-segment p-adic arithmetic shares with residue arithmetic the property that it is free of rounding errors.

Author : Stephen Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Page : 477 pages
File Size : 50,7 Mb
Release : 2018-06-07
Category : Business & Economics
ISBN : 9781316518960

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Introduction to Applied Linear Algebra by Stephen Boyd,Lieven Vandenberghe Pdf

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Author : Leslie Hogben
Publisher : CRC Press
Page : 1838 pages
File Size : 52,8 Mb
Release : 2013-11-26
Category : Mathematics
ISBN : 9781466507296

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Handbook of Linear Algebra by Leslie Hogben Pdf

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

Author : Stephen J. Kirkland,Michael Neumann
Publisher : CRC Press
Page : 330 pages
File Size : 41,7 Mb
Release : 2012-12-18
Category : Mathematics
ISBN : 9781439888599

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Group Inverses of M-Matrices and Their Applications by Stephen J. Kirkland,Michael Neumann Pdf

Group inverses for singular M-matrices are useful tools not only in matrix analysis, but also in the analysis of stochastic processes, graph theory, electrical networks, and demographic models. Group Inverses of M-Matrices and Their Applications highlights the importance and utility of the group inverses of M-matrices in several application areas.

Author : László T. Kóczy,Jesús Medina-Moreno,Eloísa Ramírez-Poussa
Publisher : Springer
Page : 138 pages
File Size : 40,8 Mb
Release : 2018-11-02
Category : Technology & Engineering
ISBN : 9783030016326

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Interactions Between Computational Intelligence and Mathematics Part 2 by László T. Kóczy,Jesús Medina-Moreno,Eloísa Ramírez-Poussa Pdf

This book presents recent research in the field of interaction between computational intelligence and mathematics. In the current technological age, we face the challenges of tackling very complex problems – in the usual sense, but also in the mathematical and theoretical computer science sense. However, even the most up-to-date results in mathematics, are unable to provide exact solutions of such problems, and no further technical advances will ever make it possible to find general and exact solutions. Constantly developing technologies (including social technologies) necessitate handling very complex problems. This has led to a search for acceptably “good” or precise solutions, which can be achieved by the combination of traditional mathematical techniques and computational intelligence tools, in order to solve the various problems emerging in many different areas to a satisfactory degree. Important funding programs, such as the European Commission’s current framework programme for research and innovation – Horizon 2020 – are devoted to the development of new instruments to deal with the current challenges. Without doubt, research topics associated with the interactions between computational intelligence and traditional mathematics play a key role. Presenting contributions from engineers, scientists and mathematicians, this book offers a series of novel solutions for meaningful and real-world problems that connect those research areas.