Matrices And Matroids For Systems Analysis
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Matrices And Matroids For Systems Analysis
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Author : Kazuo Murota
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-27
Matrices And Matroids For Systems Analysis written by Kazuo Murota 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 2009-10-27 with Mathematics categories.
A matroid is an abstract mathematical structure that captures combinatorial properties of matrices. This book offers a unique introduction to matroid theory, emphasizing motivations from matrix theory and applications to systems analysis. This book serves also as a comprehensive presentation of the theory and application of mixed matrices, developed primarily by the present author in the 1990's. A mixed matrix is a convenient mathematical tool for systems analysis, compatible with the physical observation that "fixed constants" and "system parameters" are to be distinguished in the description of engineering systems. This book will be extremely useful to graduate students and researchers in engineering, mathematics and computer science. From the reviews: "...The book has been prepared very carefully, contains a lot of interesting results and is highly recommended for graduate and postgraduate students." András Recski, Mathematical Reviews Clippings 2000m:93006
Systems Analysis By Graphs And Matroids
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Author : Kazuo Murota
language : en
Publisher:
Release Date : 1987
Systems Analysis By Graphs And Matroids written by Kazuo Murota and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Graph theory categories.
Systems Analysis By Graphs And Matroids
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Author : Kazuo Murota
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Systems Analysis By Graphs And Matroids written by Kazuo Murota 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 2012-12-06 with Mathematics categories.
Recent technology involves large-scale physical or engineering systems consisting of thousands of interconnected elementary units. This monograph illustrates how engineering problems can be solved using the recent results of combinatorial mathematics through appropriate mathematical modeling. The structural solvability of a system of linear or nonlinear equations as well as the structural controllability of a linear time-invariant dynamical system are treated by means of graphs and matroids. Special emphasis is laid on the importance of relevant physical observations to successful mathematical modelings. The reader will become acquainted with the concepts of matroid theory and its corresponding matroid theoretical approach. This book is of interest to graduate students and researchers.
Introduction To The Theory Of Matroids
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Author : R. v. Randow
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To The Theory Of Matroids written by R. v. Randow 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 2012-12-06 with Business & Economics categories.
Matroid theory has its origin in a paper by H. Whitney entitled "On the abstract properties of linear dependence" [35], which appeared in 1935. The main objective of the paper was to establish the essential (abstract) properties of the concepts of linear dependence and independence in vector spaces, and to use these for the axiomatic definition of a new algebraic object, namely the matroid. Furthermore, Whitney showed that these axioms are also abstractions of certain graph-theoretic concepts. This is very much in evidence when one considers the basic concepts making up the structure of a matroid: some reflect their linear algebraic origin, while others reflect their graph-theoretic origin. Whitney also studied a number of important examples of matroids. The next major development was brought about in the forties by R. Rado's matroid generalisation of P. Hall's famous "marriage" theorem. This provided new impulses for transversal theory, in which matroids today play an essential role under the name of "independence structures", cf. the treatise on transversal theory by L. Mirsky [26J. At roughly the same time R.P. Dilworth estab lished the connection between matroids and lattice theory. Thus matroids became an essential part of combinatorial mathematics. About ten years later W.T. Tutte [30] developed the funda mentals of matroids in detail from a graph-theoretic point of view, and characterised graphic matroids as well as the larger class of those matroids that are representable over any field.
Introduction To The Theory Of Matroids
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Author : W. T. Tutte
language : en
Publisher: Elsevier Publishing Company
Release Date : 1971
Introduction To The Theory Of Matroids written by W. T. Tutte and has been published by Elsevier Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.
Topics In Matroid Theory
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Author : Leonidas S. Pitsoulis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-24
Topics In Matroid Theory written by Leonidas S. Pitsoulis 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 2013-10-24 with Mathematics categories.
Topics in Matroid Theory provides a brief introduction to matroid theory with an emphasis on algorithmic consequences.Matroid theory is at the heart of combinatorial optimization and has attracted various pioneers such as Edmonds, Tutte, Cunningham and Lawler among others. Matroid theory encompasses matrices, graphs and other combinatorial entities under a common, solid algebraic framework, thereby providing the analytical tools to solve related difficult algorithmic problems. The monograph contains a rigorous axiomatic definition of matroids along with other necessary concepts such as duality, minors, connectivity and representability as demonstrated in matrices, graphs and transversals. The author also presents a deep decomposition result in matroid theory that provides a structural characterization of graphic matroids, and show how this can be extended to signed-graphic matroids, as well as the immediate algorithmic consequences.
Integer Programming And Combinatorial Optimization
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Author : Oktay Günlük
language : en
Publisher: Springer
Release Date : 2011-06-21
Integer Programming And Combinatorial Optimization written by Oktay Günlük and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-21 with Computers categories.
This book constitutes the proceedings of the 15th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2011, held in New York, USA in June 2011. The 33 papers presented were carefully reviewed and selected from 110 submissions. The conference is a forum for researchers and practitioners working on various aspects of integer programming and combinatorial optimization with the aim to present recent developments in theory, computation, and applications. The scope of IPCO is viewed in a broad sense, to include algorithmic and structural results in integer programming and combinatorial optimization as well as revealing computational studies and novel applications of discrete optimization to practical problems.
Combinatorial And Graph Theoretical Problems In Linear Algebra
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Author : Richard A. Brualdi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Combinatorial And Graph Theoretical Problems In Linear Algebra written by Richard A. Brualdi 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 2012-12-06 with Mathematics categories.
This IMA Volume in Mathematics and its Applications COMBINATORIAL AND GRAPH-THEORETICAL PROBLEMS IN LINEAR ALGEBRA is based on the proceedings of a workshop that was an integral part of the 1991-92 IMA program on "Applied Linear Algebra." We are grateful to Richard Brualdi, George Cybenko, Alan George, Gene Golub, Mitchell Luskin, and Paul Van Dooren for planning and implementing the year-long program. We especially thank Richard Brualdi, Shmuel Friedland, and Victor Klee for organizing this workshop and editing the proceedings. The financial support of the National Science Foundation made the workshop possible. A vner Friedman Willard Miller, Jr. PREFACE The 1991-1992 program of the Institute for Mathematics and its Applications (IMA) was Applied Linear Algebra. As part of this program, a workshop on Com binatorial and Graph-theoretical Problems in Linear Algebra was held on November 11-15, 1991. The purpose of the workshop was to bring together in an informal setting the diverse group of people who work on problems in linear algebra and matrix theory in which combinatorial or graph~theoretic analysis is a major com ponent. Many of the participants of the workshop enjoyed the hospitality of the IMA for the entire fall quarter, in which the emphasis was discrete matrix analysis.
Sparsity
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Author : A. Brameller
language : en
Publisher: Pitman Publishing
Release Date : 1976
Sparsity written by A. Brameller and has been published by Pitman Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.
Introduction To Linear Systems Analysis
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Author : George M. Swisher
language : en
Publisher: Matrix Publishers, Incorporated
Release Date : 1976
Introduction To Linear Systems Analysis written by George M. Swisher and has been published by Matrix Publishers, Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Science categories.