Polynomial And Matrix Computations
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Polynomial And Matrix Computations
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Author : Dario Bini
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Polynomial And Matrix Computations written by Dario Bini 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.
Our Subjects and Objectives. This book is about algebraic and symbolic computation and numerical computing (with matrices and polynomials). It greatly extends the study of these topics presented in the celebrated books of the seventies, [AHU] and [BM] (these topics have been under-represented in [CLR], which is a highly successful extension and updating of [AHU] otherwise). Compared to [AHU] and [BM] our volume adds extensive material on parallel com putations with general matrices and polynomials, on the bit-complexity of arithmetic computations (including some recent techniques of data compres sion and the study of numerical approximation properties of polynomial and matrix algorithms), and on computations with Toeplitz matrices and other dense structured matrices. The latter subject should attract people working in numerous areas of application (in particular, coding, signal processing, control, algebraic computing and partial differential equations). The au thors' teaching experience at the Graduate Center of the City University of New York and at the University of Pisa suggests that the book may serve as a text for advanced graduate students in mathematics and computer science who have some knowledge of algorithm design and wish to enter the exciting area of algebraic and numerical computing. The potential readership may also include algorithm and software designers and researchers specializing in the design and analysis of algorithms, computational complexity, alge braic and symbolic computing, and numerical computation.
Polynomial And Matrix Computations
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Author : Dario Bini
language : en
Publisher:
Release Date : 1994
Polynomial And Matrix Computations written by Dario Bini and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Matrices categories.
Matrix Computations
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Author : Gene Howard Golub
language : en
Publisher:
Release Date : 1996
Matrix Computations written by Gene Howard Golub and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Matrices categories.
Revised and updated, the third edition of Golub and Van Loan's classic text in computer science provides essential information about the mathematical background and algorithmic skills required for the production of numerical software. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to handle the sparse unsymmetric linear system problem.
Error Free Polynomial Matrix Computations
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Author : E.V. Krishnamurthy
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Error Free Polynomial Matrix Computations written by E.V. Krishnamurthy 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 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.
Matrix Polynomials
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Author : I. Gohberg
language : en
Publisher: SIAM
Release Date : 2009-07-23
Matrix Polynomials written by I. Gohberg and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-23 with Mathematics categories.
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.
Matrices Moments And Quadrature With Applications
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Author : Gene H. Golub
language : en
Publisher: Princeton University Press
Release Date : 2009-12-07
Matrices Moments And Quadrature With Applications written by Gene H. Golub and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-07 with Mathematics categories.
This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part. Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization. This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.
Numerical Polynomial Algebra
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Author : Hans J. Stetter
language : en
Publisher: SIAM
Release Date : 2004-01-01
Numerical Polynomial Algebra written by Hans J. Stetter and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Mathematics categories.
In many important areas of scientific computing, polynomials in one or more variables are employed in the mathematical modeling of real-life phenomena; yet most of classical computer algebra assumes exact rational data. This book is the first comprehensive treatment of the emerging area of numerical polynomial algebra, an area that falls between classical numerical analysis and classical computer algebra but, surprisingly, has received little attention so far. The author introduces a conceptual framework that permits the meaningful solution of various algebraic problems with multivariate polynomial equations whose coefficients have some indeterminacy; for this purpose, he combines approaches of both numerical linear algebra and commutative algebra. For the application scientist, Numerical Polynomial Algebra provides both a survey of polynomial problems in scientific computing that may be solved numerically and a guide to their numerical treatment. In addition, the book provides both introductory sections and novel extensions of numerical analysis and computer algebra, making it accessible to the reader with expertise in either one of these areas.
Counting Polynomial Matrices Over Finite Fields
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Author : Julia Lieb
language : en
Publisher: BoD – Books on Demand
Release Date : 2017-09-15
Counting Polynomial Matrices Over Finite Fields written by Julia Lieb and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-15 with Mathematics categories.
This book is dealing with three mathematical areas, namely polynomial matrices over finite fields, linear systems and coding theory. Primeness properties of polynomial matrices provide criteria for the reachability and observability of interconnected linear systems. Since time-discrete linear systems over finite fields and convolutional codes are basically the same objects, these results could be transferred to criteria for non-catastrophicity of convolutional codes. In particular, formulas for the number of pairwise coprime polynomials and for the number of mutually left coprime polynomial matrices are calculated. This leads to the probability that a parallel connected linear system is reachable and that a parallel connected convolutional code is non-catastrophic. Moreover, other networks of linear systems and convolutional codes are considered.
Linear Algebra And Matrix Computations With Matlab
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Author : Dingyü Xue
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-03-23
Linear Algebra And Matrix Computations With Matlab written by Dingyü Xue and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-23 with Computers categories.
This book focuses the solutions of linear algebra and matrix analysis problems, with the exclusive use of MATLAB. The topics include representations, fundamental analysis, transformations of matrices, matrix equation solutions as well as matrix functions. Attempts on matrix and linear algebra applications are also explored.
Functions Of Matrices
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Author : Nicholas J. Higham
language : en
Publisher: SIAM
Release Date : 2008-01-01
Functions Of Matrices written by Nicholas J. Higham and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
A thorough and elegant treatment of the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms. Key features include a detailed treatment of the matrix sign function and matrix roots; a development of the theory of conditioning and properties of the Fre;chet derivative; Schur decomposition; block Parlett recurrence; a thorough analysis of the accuracy, stability, and computational cost of numerical methods; general results on convergence and stability of matrix iterations; and a chapter devoted to the f(A)b problem. Ideal for advanced courses and for self-study, its broad content, references and appendix also make this book a convenient general reference. Contains an extensive collection of problems with solutions and MATLAB implementations of key algorithms.