Author: Abraham Berman
Publisher: SIAM
ISBN: 0898713218
Category : Mathematics
Languages : en
Pages : 357

Get Book Here

Book Description
Mathematics of Computing -- Numerical Analysis.

Author: Abraham Berman
Publisher: Academic Press
ISBN: 1483260860
Category : Mathematics
Languages : en
Pages : 337

Get Book Here

Book Description
Nonnegative Matrices in the Mathematical Sciences provides information pertinent to the fundamental aspects of the theory of nonnegative matrices. This book describes selected applications of the theory to numerical analysis, probability, economics, and operations research. Organized into 10 chapters, this book begins with an overview of the properties of nonnegative matrices. This text then examines the inverse-positive matrices. Other chapters consider the basic approaches to the study of nonnegative matrices, namely, geometrical and combinatorial. This book discusses as well some useful ideas from the algebraic theory of semigroups and considers a canonical form for nonnegative idempotent matrices and special types of idempotent matrices. The final chapter deals with the linear complementary problem (LCP). This book is a valuable resource for mathematical economists, mathematical programmers, statisticians, mathematicians, and computer scientists.

Author: Abraham Berman
Publisher: SIAM
ISBN: 9781611971262
Category : Mathematics
Languages : en
Pages : 360

Get Book Here

Book Description
Here is a valuable text and research tool for scientists and engineers who use or work with theory and computation associated with practical problems relating to Markov chains and queuing networks, economic analysis, or mathematical programming. Originally published in 1979, this new edition adds material that updates the subject relative to developments from 1979 to 1993. Theory and applications of nonnegative matrices are blended here, and extensive references are included in each area. You will be led from the theory of positive operators via the Perron-Frobenius theory of nonnegative matrices and the theory of inverse positivity, to the widely used topic of M-matrices. On the way, semigroups of nonnegative matrices and symmetric nonnegative matrices are discussed. Later, applications of nonnegativity and M-matrices are given; for numerical analysis the example is convergence theory of iterative methods, for probability and statistics the examples are finite Markov chains and queuing network models, for mathematical economics the example is input-output models, and for mathematical programming the example is the linear complementarity problem. Nonnegativity constraints arise very naturally throughout the physical world. Engineers, applied mathematicians, and scientists who encounter nonnegativity or generalizations of nonegativity in their work will benefit from topics covered here, connecting them to relevant theory. Researchers in one area, such as queuing theory, may find useful the techniques involving nonnegative matrices used by researchers in another area, say, mathematical programming. Exercises and biographical notes are included with each chapter.

Author: Richard S Varga
Publisher: Springer Science & Business Media
ISBN: 3642051561
Category : Mathematics
Languages : en
Pages : 363

Get Book Here

Book Description
This book is a revised version of the first edition, regarded as a classic in its field. In some places, newer research results have been incorporated in the revision, and in other places, new material has been added to the chapters in the form of additional up-to-date references and some recent theorems to give readers some new directions to pursue.

Author: Shaun M. Fallat
Publisher: Princeton University Press
ISBN: 1400839017
Category : Mathematics
Languages : en
Pages : 265

Get Book Here

Book Description
Totally nonnegative matrices arise in a remarkable variety of mathematical applications. This book is a comprehensive and self-contained study of the essential theory of totally nonnegative matrices, defined by the nonnegativity of all subdeterminants. It explores methodological background, historical highlights of key ideas, and specialized topics. The book uses classical and ad hoc tools, but a unifying theme is the elementary bidiagonal factorization, which has emerged as the single most important tool for this particular class of matrices. Recent work has shown that bidiagonal factorizations may be viewed in a succinct combinatorial way, leading to many deep insights. Despite slow development, bidiagonal factorizations, along with determinants, now provide the dominant methodology for understanding total nonnegativity. The remainder of the book treats important topics, such as recognition of totally nonnegative or totally positive matrices, variation diminution, spectral properties, determinantal inequalities, Hadamard products, and completion problems associated with totally nonnegative or totally positive matrices. The book also contains sample applications, an up-to-date bibliography, a glossary of all symbols used, an index, and related references.

Author: Aihui Zhou
Publisher: World Scientific Publishing Company
ISBN: 981310743X
Category : Mathematics
Languages : en
Pages : 362

Get Book Here

Book Description
Nonnegative matrices and positive operators are widely applied in science, engineering, and technology. This book provides the basic theory and several typical modern science and engineering applications of nonnegative matrices and positive operators, including the fundamental theory, methods, numerical analysis, and applications in the Google search engine, computational molecular dynamics, and wireless communications.Unique features of this book include the combination of the theories of nonnegative matrices and positive operators as well as the emphasis on applications of nonnegative matrices in the numerical analysis of positive operators, such as Markov operators and Frobenius-Perron operators both of which play key roles in the statistical and stochastic studies of dynamical systems.It can be used as a textbook for an upper level undergraduate or beginning graduate course in advanced matrix theory and/or positive operators as well as for an advanced topics course in operator theory or ergodic theory. In addition, it serves as a good reference for researchers in mathematical sciences, physical sciences, and engineering.

Author: R. B. Bapat
Publisher: Cambridge University Press
ISBN: 0521571677
Category : Mathematics
Languages : en
Pages : 351

Get Book Here

Book Description
This book provides an integrated treatment of the theory of nonnegative matrices (matrices with only positive numbers or zero as entries) and some related classes of positive matrices, concentrating on connections with game theory, combinatorics, inequalities, optimisation and mathematical economics. The wide variety of applications, which include price fixing, scheduling and the fair division problem, have been carefully chosen both for their elegant mathematical content and for their accessibility to students with minimal preparation. Many results in matrix theory are also presented. The treatment is rigorous and almost all results are proved completely. These results and applications will be of great interest to researchers in linear programming, statistics and operations research. The minimal prerequisites also make the book accessible to first-year graduate students.

Author: Abraham Berman
Publisher:
ISBN: 9781483236094
Category : Non-negative matrices
Languages : en
Pages : 0

Get Book Here

Book Description

Author: E. Seneta
Publisher: Springer Science & Business Media
ISBN: 0387327924
Category : Mathematics
Languages : en
Pages : 295

Get Book Here

Book Description
Since its inception by Perron and Frobenius, the theory of non-negative matrices has developed enormously and is now being used and extended in applied fields of study as diverse as probability theory, numerical analysis, demography, mathematical economics, and dynamic programming, while its development is still proceeding rapidly as a branch of pure mathematics in its own right. While there are books which cover this or that aspect of the theory, it is nevertheless not uncommon for workers in one or another branch of its development to be unaware of what is known in other branches, even though there is often formal overlap. One of the purposes of this book is to relate several aspects of the theory, insofar as this is possible. The author hopes that the book will be useful to mathematicians; but in particular to the workers in applied fields, so the mathematics has been kept as simple as could be managed. The mathematical requisites for reading it are: some knowledge of real-variable theory, and matrix theory; and a little knowledge of complex-variable; the emphasis is on real-variable methods. (There is only one part of the book, the second part of 55.5, which is of rather specialist interest, and requires deeper knowledge.) Appendices provide brief expositions of those areas of mathematics needed which may be less g- erally known to the average reader.

Author: Stephen Boyd
Publisher: Cambridge University Press
ISBN: 1316518965
Category : Business & Economics
Languages : en
Pages : 477

Get Book Here

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