Factorization

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Factorization and Integrable Systems

Israel Gohberg,Nenad Manojlovic,Antonio, F. dos Santos
Factorization and Integrable Systems Book PDF

Author : Israel Gohberg,Nenad Manojlovic,Antonio, F. dos Santos
Publisher : Birkhäuser
Page : 227 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880039

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Factorization and Integrable Systems by Israel Gohberg,Nenad Manojlovic,Antonio, F. dos Santos Pdf

This volume comprises the specially prepared lecture notes of a a Summer School on "Factorization and Integrable Systems" held in September 2000 at the University of Algarve in Portugal. The main aim of the school was to review the modern factorization theory and its application to classical and quantum integrable systems. The program consisted of a number of short courses given by leading experts in the field.

Factorization in Integral Domains

Daniel Anderson
Factorization in Integral Domains Book PDF

Author : Daniel Anderson
Publisher : Routledge
Page : 448 pages
File Size : 46,6 Mb
Release : 2017-11-13
Category : Mathematics
ISBN : 9781351448949

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Factorization in Integral Domains by Daniel Anderson Pdf

The contents in this work are taken from both the University of Iowa's Conference on Factorization in Integral Domains, and the 909th Meeting of the American Mathematical Society's Special Session in Commutative Ring Theory held in Iowa City. The text gathers current work on factorization in integral domains and monoids, and the theory of divisibility, emphasizing possible different lengths of factorization into irreducible elements.

Constructive Methods of Wiener-Hopf Factorization

Gohberg,Kaashoek
Constructive Methods of Wiener Hopf Factorization Book PDF

Author : Gohberg,Kaashoek
Publisher : Birkhäuser
Page : 418 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034874182

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Constructive Methods of Wiener-Hopf Factorization by Gohberg,Kaashoek Pdf

The main part of this paper concerns Toeplitz operators of which the symbol W is an m x m matrix function defined on a disconnected curve r. The curve r is assumed to be the union of s + 1 nonintersecting simple smooth closed contours rOo r •. . . • rs which form the positively l oriented boundary of a finitely connected bounded domain in t. Our main requirement on the symbol W is that on each contour rj the function W is the restriction of a rational matrix function Wj which does not have poles and zeros on rj and at infinity. Using the realization theorem from system theory (see. e. g . • [1]. Chapter 2) the rational matrix function Wj (which differs from contour to contour) may be written in the form 1 (0. 1) W . (A) = I + C. (A - A. f B. A E r· J J J J J where Aj is a square matrix of size nj x n• say. B and C are j j j matrices of sizes n. x m and m x n . • respectively. and the matrices A. J x J J and Aj = Aj - BjC have no eigenvalues on r . (In (0. 1) the functions j j Wj are normalized to I at infinity.

Factorization of Matrix and Operator Functions: The State Space Method

Harm Bart,Israel Gohberg,Marinus A. Kaashoek,André C.M. Ran
Factorization of Matrix and Operator Functions The State Space Method Book PDF

Author : Harm Bart,Israel Gohberg,Marinus A. Kaashoek,André C.M. Ran
Publisher : Springer Science & Business Media
Page : 409 pages
File Size : 52,5 Mb
Release : 2007-12-20
Category : Mathematics
ISBN : 9783764382681

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Factorization of Matrix and Operator Functions: The State Space Method by Harm Bart,Israel Gohberg,Marinus A. Kaashoek,André C.M. Ran Pdf

This book delineates the various types of factorization problems for matrix and operator functions. The problems originate from, or are motivated by, the theory of non-selfadjoint operators, the theory of matrix polynomials, mathematical systems and control theory, the theory of Riccati equations, inversion of convolution operators, and the theory of job scheduling in operations research. The book presents a geometric principle of factorization which has its origins in the state space theory of linear input-output systems and in the theory of characteristic operator functions.

Non-negative Matrix Factorization Techniques

Ganesh R. Naik
Non negative Matrix Factorization Techniques Book PDF

Author : Ganesh R. Naik
Publisher : Springer
Page : 194 pages
File Size : 54,8 Mb
Release : 2015-09-25
Category : Technology & Engineering
ISBN : 9783662483312

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Non-negative Matrix Factorization Techniques by Ganesh R. Naik Pdf

This book collects new results, concepts and further developments of NMF. The open problems discussed include, e.g. in bioinformatics: NMF and its extensions applied to gene expression, sequence analysis, the functional characterization of genes, clustering and text mining etc. The research results previously scattered in different scientific journals and conference proceedings are methodically collected and presented in a unified form. While readers can read the book chapters sequentially, each chapter is also self-contained. This book can be a good reference work for researchers and engineers interested in NMF, and can also be used as a handbook for students and professionals seeking to gain a better understanding of the latest applications of NMF.

Abstract Band Method via Factorization, Positive and Band Extensions of Multivariable Almost Periodic Matrix Functions, and Spectral Estimation

L. Rodman,Ilya M. Spitkovskiĭ,Hugo Jan Woerdeman
Abstract Band Method via Factorization Positive and Band Extensions of Multivariable Almost Periodic Matrix Functions and Spectral Estimation Book PDF

Author : L. Rodman,Ilya M. Spitkovskiĭ,Hugo Jan Woerdeman
Publisher : American Mathematical Soc.
Page : 71 pages
File Size : 54,9 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821829967

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Abstract Band Method via Factorization, Positive and Band Extensions of Multivariable Almost Periodic Matrix Functions, and Spectral Estimation by L. Rodman,Ilya M. Spitkovskiĭ,Hugo Jan Woerdeman Pdf

New versions are developed of an abstract scheme, which are designed to provide a framework for solving a variety of extension problems. The abstract scheme is commonly known as the band method. The main feature of the new versions is that they express directly the conditions for existence of positive band extensions in terms of abstract factorizations (with certain additional properties). The results allow us to prove, among other things, that the band extension is continuous in an appropriate sense. Using the new versions of the abstract band method, we solve the positive extension problem for almost periodic matrix functions of several real variables with Fourier coefficients indexed in a given additive subgroup of the space of variables.This generality allows us to treat simultaneously many particular cases, for example the case of functions periodic in some variables and almost periodic in others. Necessary and sufficient conditions are given for the existence of positive extensions in terms of Toeplitz operators on Besikovitch spaces. Furthermore, when a solution exists a special extension (the band extension) is constructed which enjoys a maximum entropy property.A linear fractional parameterization of the set of all extensions is also provided. We interpret the obtained results (in the periodic case) in terms of existence of a multivariate autoregressive moving averages (ARMA) process with given autocorrelation coefficients, and identify its maximal prediction error. Another application concerns the solution of the positive extension problem in the context of Wiener algebra of infinite operator matrices. It includes the identification of the maximum entropy extension and a description of all positive extensions via a linear fractional formula. In the periodic case it solves a linear estimation problem for cyclostationary stochastic processes.

Factorization of Matrix Functions and Singular Integral Operators

Prof. Kevin F. Clancey,Prof. Israel Gohberg
Factorization of Matrix Functions and Singular Integral Operators Book PDF

Author : Prof. Kevin F. Clancey,Prof. Israel Gohberg
Publisher : Birkhäuser
Page : 246 pages
File Size : 42,6 Mb
Release : 2013-11-21
Category : Science
ISBN : 9783034854924

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Factorization of Matrix Functions and Singular Integral Operators by Prof. Kevin F. Clancey,Prof. Israel Gohberg Pdf

A few years aga the authors started a project of a book on the theory of systems of one-dimensional singular integral equa tions which was planned as a continuation of the monograph by one of the authors and N. Ya. Krupnik ~~ concerning scalar equa tions. This set of notes was initiated as a chapter dealing with problems of factorization of matrix functions vis-a-vis appli cations to systems of singular integral equations. Working systematically onthischapter and adding along the way new points of view, new proofs and results, we finally saw that the material connected with factorizations is of independent interest and we decided to publish this chapter as aseparate volume. In fact, because of recent activity, the amount of material was quite large and we quickly learned that we cannot cover all of the results in complete detail. We have tried to include a represen tative variety of all kinds of methods, techniques,results and applications. Apart of the current work exposes results from the Russian literature which have never appeared in English translation. We have also decided to reflect some of the recent results which make interesting connections between factorization of matrix functions and systems theory. The field remains very active and many results and connec tions are still not weIl understood. These notes should be viewed as a stepping stone to further development. The authors hope that sometime they will return to complete their original plan.

Singular Integral Operators, Factorization and Applications

Albrecht Böttcher,Marinus A. Kaashoek,Amarino Brites Lebre,Antonio, F. dos Santos,Frank-Olme Speck
Singular Integral Operators Factorization and Applications Book PDF

Author : Albrecht Böttcher,Marinus A. Kaashoek,Amarino Brites Lebre,Antonio, F. dos Santos,Frank-Olme Speck
Publisher : Birkhäuser
Page : 393 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880077

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Singular Integral Operators, Factorization and Applications by Albrecht Böttcher,Marinus A. Kaashoek,Amarino Brites Lebre,Antonio, F. dos Santos,Frank-Olme Speck Pdf

This volume contains the proceedings of the International Workshop on Operator Theory and Applications held at the University of Algarve in Faro, Portugal, September 12-15, in the year 2000. The main topics of the conference were !> Factorization Theory; !> Factorization and Integrable Systems; !> Operator Theoretical Methods in Diffraction Theory; !> Algebraic Techniques in Operator Theory; !> Applications to Mathematical Physics and Related Topics. A total of 94 colleagues from 21 countries participated in the conference. The major part of participants came from Portugal (32), Germany (17), Israel (6), Mexico (6), the Netherlands (5), USA (4) and Austria (4). The others were from Ukraine, Venezuela (3 each), Spain, Sweden (2 each), Algeria, Australia, Belorussia, France, Georgia, Italy, Japan, Kuwait, Russia and Turkey (one of each country). It was the 12th meeting in the framework of the IWOTA conferences which started in 1981 on an initiative of Professors 1. Gohberg (Tel Aviv) and J. W. Helton (San Diego). Up to now, it was the largest conference in the field of Operator Theory in Portugal.

Factors and Factorizations of Graphs

Jin Akiyama,Mikio Kano
Factors and Factorizations of Graphs Book PDF

Author : Jin Akiyama,Mikio Kano
Publisher : Springer Science & Business Media
Page : 362 pages
File Size : 48,5 Mb
Release : 2011-06-23
Category : Computers
ISBN : 9783642219184

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Factors and Factorizations of Graphs by Jin Akiyama,Mikio Kano Pdf

This book chronicles the development of graph factors and factorizations. It pursues a comprehensive approach, addressing most of the important results from hundreds of findings over the last century. One of the main themes is the observation that many theorems can be proved using only a few standard proof techniques. This stands in marked contrast to the seemingly countless, complex proof techniques offered by the extant body of papers and books. In addition to covering the history and development of this area, the book offers conjectures and discusses open problems. It also includes numerous explanatory figures that enable readers to progressively and intuitively understand the most important notions and proofs in the area of factors and factorization.

Numerical Linear Algebra and Matrix Factorizations

Tom Lyche
Numerical Linear Algebra and Matrix Factorizations Book PDF

Author : Tom Lyche
Publisher : Springer Nature
Page : 376 pages
File Size : 54,5 Mb
Release : 2020-03-02
Category : Mathematics
ISBN : 9783030364687

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Numerical Linear Algebra and Matrix Factorizations by Tom Lyche Pdf

After reading this book, students should be able to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and to develop their own algorithms for solving them. Since these problems can be large and difficult to handle, much can be gained by understanding and taking advantage of special structures. This in turn requires a good grasp of basic numerical linear algebra and matrix factorizations. Factoring a matrix into a product of simpler matrices is a crucial tool in numerical linear algebra, because it allows us to tackle complex problems by solving a sequence of easier ones. The main characteristics of this book are as follows: It is self-contained, only assuming that readers have completed first-year calculus and an introductory course on linear algebra, and that they have some experience with solving mathematical problems on a computer. The book provides detailed proofs of virtually all results. Further, its respective parts can be used independently, making it suitable for self-study. The book consists of 15 chapters, divided into five thematically oriented parts. The chapters are designed for a one-week-per-chapter, one-semester course. To facilitate self-study, an introductory chapter includes a brief review of linear algebra.

One-Factorizations

W.D. Wallis
One Factorizations Book PDF

Author : W.D. Wallis
Publisher : Springer Science & Business Media
Page : 243 pages
File Size : 46,5 Mb
Release : 2013-04-17
Category : Computers
ISBN : 9781475725643

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One-Factorizations by W.D. Wallis Pdf

This book has grown out of graduate courses given by the author at Southern Illinois University, Carbondale, as well as a series of seminars delivered at Curtin University of Technology, Western Australia. The book is intended to be used both as a textbook at the graduate level and also as a professional reference. The topic of one-factorizations fits into the theory of combinatorial designs just as much as it does into graph theory. Factors and factorizations occur as building blocks in the theory of designs in a number of places. Our approach owes as much to design theory as it does to graph theory. It is expected that nearly all readers will have some background in the theory of graphs, such as an advanced undergraduate course in Graph Theory or Applied Graph Theory. However, the book is self-contained, and the first two chapters are a thumbnail sketch of basic graph theory. Many readers will merely skim these chapters, observing our notational conventions along the way. (These introductory chapters could, in fact, enable some instructors to Ilse the book for a somewhat eccentric introduction to graph theory.) Chapter 3 introduces one-factors and one-factorizations. The next two chapters outline two major application areas: combinatorial arrays and tournaments. These two related areas have provided the impetus for a good deal of study of one-factorizations.

Factorization

Steven H. Weintraub
Factorization Book PDF

Author : Steven H. Weintraub
Publisher : CRC Press
Page : 270 pages
File Size : 41,9 Mb
Release : 2008-05-15
Category : Mathematics
ISBN : 9781439865668

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Factorization by Steven H. Weintraub Pdf

The concept of factorization, familiar in the ordinary system of whole numbers that can be written as a unique product of prime numbers, plays a central role in modern mathematics and its applications. This exposition of the classic theory leads the reader to an understanding of the current knowledge of the subject and its connections to other math

Groupoid Factorizations In The Semigroup Of Binary Systems

Hiba F. Fayoumi
Groupoid Factorizations In The Semigroup Of Binary Systems Book PDF

Author : Hiba F. Fayoumi
Publisher : Infinite Study
Page : 28 pages
File Size : 40,9 Mb
Release : 2024-06-29
Category : Mathematics
ISBN : 8210379456XXX

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Groupoid Factorizations In The Semigroup Of Binary Systems by Hiba F. Fayoumi Pdf

We introduce two methods of factorization for this binary system under the binary groupoid product in the semigroup. We conclude that a strong non-idempotent groupoid can be represented as a product of its similar- and signature- derived factors. Moreover, we show that a groupoid with the orientation property is a product of its orient- and skew- factors. These unique factorizations can be useful for various applications in other areas of study. Application to algebras such as B/BCH/BCI/BCK/BH/BI/d-algebra are widely given throughout this paper.

Non-Unique Factorizations

Alfred Geroldinger,Franz Halter-Koch
Non Unique Factorizations Book PDF

Author : Alfred Geroldinger,Franz Halter-Koch
Publisher : CRC Press
Page : 723 pages
File Size : 52,5 Mb
Release : 2006-01-13
Category : Mathematics
ISBN : 9781420003208

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Non-Unique Factorizations by Alfred Geroldinger,Franz Halter-Koch Pdf

From its origins in algebraic number theory, the theory of non-unique factorizations has emerged as an independent branch of algebra and number theory. Focused efforts over the past few decades have wrought a great number and variety of results. However, these remain dispersed throughout the vast literature. For the first time, Non-Unique Factoriza