Download or read book Algebraic Operations of Polynomial Matrices written by Stephen Barnett and published by . This book was released on 1989 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Operations with Polynomial Matrices written by Peter Stefanidis and published by Springer. This book was released on 1992 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Structured Matrices and Polynomials written by Victor Y. Pan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This user-friendly, engaging textbook makes the material accessible to graduate students and new researchers who wish to study the rapidly exploding area of computations with structured matrices and polynomials. The book goes beyond research frontiers and, apart from very recent research articles, includes previously unpublished results.
Download or read book Matrix Polynomials written by I. Gohberg and published by SIAM. This book was released on 2009-07-23 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the definitive treatment of the theory of polynomials in a complex variable with matrix coefficients. Basic matrix theory can be viewed as the study of the special case of polynomials of first degree; the theory developed in Matrix Polynomials is a natural extension of this case to polynomials of higher degree. It has applications in many areas, such as differential equations, systems theory, the Wiener-Hopf technique, mechanics and vibrations, and numerical analysis. Although there have been significant advances in some quarters, this work remains the only systematic development of the theory of matrix polynomials. The book is appropriate for students, instructors, and researchers in linear algebra, operator theory, differential equations, systems theory, and numerical analysis. Its contents are accessible to readers who have had undergraduate-level courses in linear algebra and complex analysis.
Download or read book Numerical Operations with Polynomial Matrices written by Peter Stefanidis and published by Springer. This book was released on 2014-03-12 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this monograph is to describe a class of com- putational methods, based on polynomial matrices, for the design of dynamic compensators for linear multi-variable control systems. The design of the compensator, which may be either analogue or digital, is based on pole assignment. A matrix fraction description, which employs polynomial matri- ces, is used to represent the system. The design comptuta- tion, however, employs matrices of real numbers rather than polynomial matrices. This simplifies the computational pro- cedures which can thus be implementedin commercially-avai- lable software packages. Both transient and steady-state performace specifications are included in the design proce- dure which is illustrated by four detailed examples. The monograph should be of interest to research workers and engineers in the field fo multi-variable control. For the former it provides some new computational tools for the ap- plication of algebraic methods, for both groups it introdu- ces some new ideas for a more-direct approach to compensator design.
Download or read book Error Free Polynomial Matrix Computations written by E.V. Krishnamurthy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written as an introduction to polynomial matrix computa tions. It is a companion volume to an earlier book on Methods and Applications of Error-Free Computation by R. T. Gregory and myself, published by Springer-Verlag, New York, 1984. This book is intended for seniors and graduate students in computer and system sciences, and mathematics, and for researchers in the fields of computer science, numerical analysis, systems theory, and computer algebra. Chapter I introduces the basic concepts of abstract algebra, including power series and polynomials. This chapter is essentially meant for bridging the gap between the abstract algebra and polynomial matrix computations. Chapter II is concerned with the evaluation and interpolation of polynomials. The use of these techniques for exact inversion of poly nomial matrices is explained in the light of currently available error-free computation methods. In Chapter III, the principles and practice of Fourier evaluation and interpolation are described. In particular, the application of error-free discrete Fourier transforms for polynomial matrix computations is consi dered.
Download or read book College Algebra written by Jay Abramson and published by . This book was released on 2018-01-07 with total page 892 pages. Available in PDF, EPUB and Kindle. Book excerpt: College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they've learned. Coverage and Scope In determining the concepts, skills, and topics to cover, we engaged dozens of highly experienced instructors with a range of student audiences. The resulting scope and sequence proceeds logically while allowing for a significant amount of flexibility in instruction. Chapters 1 and 2 provide both a review and foundation for study of Functions that begins in Chapter 3. The authors recognize that while some institutions may find this material a prerequisite, other institutions have told us that they have a cohort that need the prerequisite skills built into the course. Chapter 1: Prerequisites Chapter 2: Equations and Inequalities Chapters 3-6: The Algebraic Functions Chapter 3: Functions Chapter 4: Linear Functions Chapter 5: Polynomial and Rational Functions Chapter 6: Exponential and Logarithm Functions Chapters 7-9: Further Study in College Algebra Chapter 7: Systems of Equations and Inequalities Chapter 8: Analytic Geometry Chapter 9: Sequences, Probability and Counting Theory
Download or read book algebraic structure and matrices written by E. A. Maxwell and published by CUP Archive. This book was released on 1969 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Polynomial and Rational Matrices written by Tadeusz Kaczorek and published by Springer Science & Business Media. This book was released on 2007-01-19 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews new results in the application of polynomial and rational matrices to continuous- and discrete-time systems. It provides the reader with rigorous and in-depth mathematical analysis of the uses of polynomial and rational matrices in the study of dynamical systems. It also throws new light on the problems of positive realization, minimum-energy control, reachability, and asymptotic and robust stability.
Download or read book The Polynomial Identities and Invariants of n times n Matrices written by Edward Formanek and published by American Mathematical Soc.. This book was released on 1991 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of polynomial identities, as a well-defined field of study, began with a well-known 1948 article of Kaplansky. The field has since developed along two branches: the structural, which investigates the properties of rings which satisfy a polynomial identity; and the varietal, which investigates the set of polynomials in the free ring which vanish under all specializations in a given ring. This book is based on lectures delivered during an NSF-CBMS Regional Conference, held at DePaul University in July 1990, at which the author was the principal lecturer. The first part of the book is concerned with polynomial identity rings. The emphasis is on those parts of the theory related to n x n matrices, including the major structure theorems and the construction of certain polynomials identities and central polynomials for n x n matrices. The ring of generic matrices and its centre is described. The author then moves on to the invariants of n x n matrices, beginning with the first and second fundamental theorems, which are used to describe the polynomial identities satisfied by n x n matrices. One of the exceptional features of this book is the way it emphasizes the connection between polynomial identities and invariants of n x n matrices. Accessible to those with background at the level of a first-year graduate course in algebra, this book gives readers an understanding of polynomial identity rings and invariant theory, as well as an indication of current problems and research in these areas.
Download or read book Structured Matrix Based Methods for Approximate Polynomial GCD written by Paola Boito and published by Springer Science & Business Media. This book was released on 2012-03-13 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Defining and computing a greatest common divisor of two polynomials with inexact coefficients is a classical problem in symbolic-numeric computation. The first part of this book reviews the main results that have been proposed so far in the literature. As usual with polynomial computations, the polynomial GCD problem can be expressed in matrix form: the second part of the book focuses on this point of view and analyses the structure of the relevant matrices, such as Toeplitz, Toepliz-block and displacement structures. New algorithms for the computation of approximate polynomial GCD are presented, along with extensive numerical tests. The use of matrix structure allows, in particular, to lower the asymptotic computational cost from cubic to quadratic order with respect to polynomial degree.
Download or read book Linear Algebra written by Harold M. Edwards and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Proposes a radically new and thoroughly algorithmic approach to linear algebra * Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples * Designed for a one-semester course, this text gives the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject
Download or read book Computer Algebra and Polynomials written by Jaime Gutierrez and published by Springer. This book was released on 2015-01-20 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra and number theory have always been counted among the most beautiful mathematical areas with deep proofs and elegant results. However, for a long time they were not considered that important in view of the lack of real-life applications. This has dramatically changed: nowadays we find applications of algebra and number theory frequently in our daily life. This book focuses on the theory and algorithms for polynomials over various coefficient domains such as a finite field or ring. The operations on polynomials in the focus are factorization, composition and decomposition, basis computation for modules, etc. Algorithms for such operations on polynomials have always been a central interest in computer algebra, as it combines formal (the variables) and algebraic or numeric (the coefficients) aspects. The papers presented were selected from the Workshop on Computer Algebra and Polynomials, which was held in Linz at the Johann Radon Institute for Computational and Applied Mathematics (RICAM) during November 25-29, 2013, at the occasion of the Special Semester on Applications of Algebra and Number Theory.
Download or read book Exploring the Extension of Natural Operations on Intervals Matrices and Complex Numbers written by W. B. Vasantha Kandasamy, Florentin Smarandache and published by Infinite Study. This book was released on 2012 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we explore the possibility of extending the natural operations on reals to intervals and matrices. The extension to intervals makes us define a natural class of intervals in which we accept [a, b], a greater than b. Further, we introduce a complex modulo integer in Z_n (n, a positive integer) and denote it by iF with iF^2 = n-1.
Download or read book Solving Systems of Polynomial Equations written by Bernd Sturmfels and published by American Mathematical Soc.. This book was released on 2002 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridging a number of mathematical disciplines, and exposing many facets of systems of polynomial equations, Bernd Sturmfels's study covers a wide spectrum of mathematical techniques and algorithms, both symbolic and numerical.
Download or read book Polynomials and the mod 2 Steenrod Algebra written by Grant Walker (Mathematician) and published by Cambridge University Press. This book was released on 2018 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to link the mod 2 Steenrod algebra, a classical object of study in algebraic topology, with modular representations of matrix groups over the field F of two elements. The link is provided through a detailed study of Peterson's 'hit problem' concerning the action of the Steenrod algebra on polynomials, which remains unsolved except in special cases. The topics range from decompositions of integers as sums of 'powers of 2 minus 1', to Hopf algebras and the Steinberg representation of GL(n,F). Volume 1 develops the structure of the Steenrod algebra from an algebraic viewpoint and can be used as a graduate-level textbook. Volume 2 broadens the discussion to include modular representations of matrix groups.
Download or read book Polynomials and Linear Control Systems written by Stephen Barnett and published by . This book was released on 1983 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: In clear, easy-to-understand language, this volume fulfills two functions: fully developing the properties of polynomials and polynomial matrices, and demonstrating their practical application to the theory of time-invariant linear control systems. By emphasizing relatively simple matrix methods, it makes this information readily accessible to readers from diverse backgrounds. The unique combination of subject matter, problems and examples, depth of coverage, and references make this volume valuable to students and applied mathematicians. Applied mathematicians, electrical engineers, operations researchers, and mathematical economists will find this volume useful.
