Polynomial And Matrix Computations

Author : Dario Bini,Victor Y. Pan
Publisher : Springer Science & Business Media
Page : 433 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461202653

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Polynomial and Matrix Computations by Dario Bini,Victor Y. Pan Pdf

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.

Author : E.V. Krishnamurthy
Publisher : Springer Science & Business Media
Page : 170 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461251187

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Error-Free Polynomial Matrix Computations by E.V. Krishnamurthy Pdf

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.

Author : Dario Bini
Publisher : Unknown
Page : 128 pages
File Size : 46,8 Mb
Release : 1994
Category : Matrices
ISBN : OCLC:715642154

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Polynomial and Matrix Computations by Dario Bini Pdf

Author : Victor Y. Pan
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201298

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Structured Matrices and Polynomials by Victor Y. Pan Pdf

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.

Author : Gene Howard Golub
Publisher : Unknown
Page : 694 pages
File Size : 50,6 Mb
Release : 1996
Category : Matrices
ISBN : 0801837391

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Matrix Computations by Gene Howard Golub Pdf

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.

Author : Zhong-Zhi Bai,Jian-Yu Pan
Publisher : SIAM
Page : 496 pages
File Size : 45,7 Mb
Release : 2021-09-09
Category : Mathematics
ISBN : 9781611976632

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Matrix Analysis and Computations by Zhong-Zhi Bai,Jian-Yu Pan Pdf

This comprehensive book is presented in two parts; the first part introduces the basics of matrix analysis necessary for matrix computations, and the second part presents representative methods and the corresponding theories in matrix computations. Among the key features of the book are the extensive exercises at the end of each chapter. Matrix Analysis and Computations provides readers with the matrix theory necessary for matrix computations, especially for direct and iterative methods for solving systems of linear equations. It includes systematic methods and rigorous theory on matrix splitting iteration methods and Krylov subspace iteration methods, as well as current results on preconditioning and iterative methods for solving standard and generalized saddle-point linear systems. This book can be used as a textbook for graduate students as well as a self-study tool and reference for researchers and engineers interested in matrix analysis and matrix computations. It is appropriate for courses in numerical analysis, numerical optimization, data science, and approximation theory, among other topics

Author : Gene H. Golub,Gérard Meurant
Publisher : Princeton University Press
Page : 376 pages
File Size : 53,9 Mb
Release : 2009-12-07
Category : Mathematics
ISBN : 9781400833887

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Matrices, Moments and Quadrature with Applications by Gene H. Golub,Gérard Meurant Pdf

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.

Author : Gene H. Golub,Charles F. Van Loan
Publisher : JHU Press
Page : 734 pages
File Size : 40,6 Mb
Release : 1996-10-15
Category : Mathematics
ISBN : 0801854148

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Matrix Computations by Gene H. Golub,Charles F. Van Loan Pdf

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.

Author : John Rischard Rice
Publisher : McGraw-Hill Companies
Page : 280 pages
File Size : 46,7 Mb
Release : 1981
Category : Computers
ISBN : UOM:39015000961592

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Matrix Computations and Mathematical Software by John Rischard Rice Pdf

Linear algebra background; types and sources of matrix computational problems; type of matrix that arise; gauss elimination and LU factorization; mathematical software objectives; mathematical software performance evaluation; how do you know you have right answers?; conditioning and backward error analysis; iterative methods; linear least squares and regression; projects; standard linear algebra software.

Author : Paola Boito
Publisher : Springer Science & Business Media
Page : 208 pages
File Size : 49,7 Mb
Release : 2012-03-13
Category : Mathematics
ISBN : 9788876423819

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Structured Matrix Based Methods for Approximate Polynomial GCD by Paola Boito Pdf

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.

Author : Ivan Stanimirović
Publisher : CRC Press
Page : 199 pages
File Size : 40,5 Mb
Release : 2017-12-14
Category : Mathematics
ISBN : 9781351630054

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Computation of Generalized Matrix Inverses and Applications by Ivan Stanimirović Pdf

This volume offers a gradual exposition to matrix theory as a subject of linear algebra. It presents both the theoretical results in generalized matrix inverses and the applications. The book is as self-contained as possible, assuming no prior knowledge of matrix theory and linear algebra. The book first addresses the basic definitions and concepts of an arbitrary generalized matrix inverse with special reference to the calculation of {i,j,...,k} inverse and the Moore–Penrose inverse. Then, the results of LDL* decomposition of the full rank polynomial matrix are introduced, along with numerical examples. Methods for calculating the Moore–Penrose’s inverse of rational matrix are presented, which are based on LDL* and QDR decompositions of the matrix. A method for calculating the A(2)T;S inverse using LDL* decomposition using methods is derived as well as the symbolic calculation of A(2)T;S inverses using QDR factorization. The text then offers several ways on how the introduced theoretical concepts can be applied in restoring blurred images and linear regression methods, along with the well-known application in linear systems. The book also explains how the computation of generalized inverses of matrices with constant values is performed. It covers several methods, such as methods based on full-rank factorization, Leverrier–Faddeev method, method of Zhukovski, and variations of the partitioning method.

Author : Hans J. Stetter
Publisher : SIAM
Page : 475 pages
File Size : 46,5 Mb
Release : 2004-05-01
Category : Mathematics
ISBN : 9780898715576

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Numerical Polynomial Algebra by Hans J. Stetter Pdf

This book is the first comprehensive treatment of numerical polynomial algebra, an area which so far has received little attention.

Author : Raymond Chan,Chen Greif,Dianne O'Leary
Publisher : OUP Oxford
Page : 581 pages
File Size : 46,9 Mb
Release : 2007-02-22
Category : Mathematics
ISBN : 9780191525773

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Milestones in Matrix Computation by Raymond Chan,Chen Greif,Dianne O'Leary Pdf

The text presents and discusses some of the most influential papers in Matrix Computation authored by Gene H. Golub, one of the founding fathers of the field. The collection of 21 papers is divided into five main areas: iterative methods for linear systems, solution of least squares problems, matrix factorizations and applications, orthogonal polynomials and quadrature, and eigenvalue problems. Commentaries for each area are provided by leading experts: Anne Greenbaum, Ake Bjorck, Nicholas Higham, Walter Gautschi, and G. W. (Pete) Stewart. Comments on each paper are also included by the original authors, providing the reader with historical information on how the paper came to be written and under what circumstances the collaboration was undertaken. Including a brief biography and facsimiles of the original papers, this text will be of great interest to students and researchers in numerical analysis and scientific computation.

Author : Richard Zippel
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461531883

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Effective Polynomial Computation by Richard Zippel Pdf

Effective Polynomial Computation is an introduction to the algorithms of computer algebra. It discusses the basic algorithms for manipulating polynomials including factoring polynomials. These algorithms are discussed from both a theoretical and practical perspective. Those cases where theoretically optimal algorithms are inappropriate are discussed and the practical alternatives are explained. Effective Polynomial Computation provides much of the mathematical motivation of the algorithms discussed to help the reader appreciate the mathematical mechanisms underlying the algorithms, and so that the algorithms will not appear to be constructed out of whole cloth. Preparatory to the discussion of algorithms for polynomials, the first third of this book discusses related issues in elementary number theory. These results are either used in later algorithms (e.g. the discussion of lattices and Diophantine approximation), or analogs of the number theoretic algorithms are used for polynomial problems (e.g. Euclidean algorithm and p-adic numbers). Among the unique features of Effective Polynomial Computation is the detailed material on greatest common divisor and factoring algorithms for sparse multivariate polynomials. In addition, both deterministic and probabilistic algorithms for irreducibility testing of polynomials are discussed.

Author : David S. Watkins
Publisher : Unknown
Page : 476 pages
File Size : 53,7 Mb
Release : 1991-01-16
Category : Mathematics
ISBN : STANFORD:36105031244911

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Fundamentals of Matrix Computations by David S. Watkins Pdf

The use of numerical methods continues to expand rapidly. At their heart lie matrix computations. Written in a clear, expository style, it allows students and professionals to build confidence in themselves by putting the theory behind matrix computations into practice instantly. Algorithms that allow students to work examples and write programs introduce each chapter. The book then moves on to discuss more complicated theoretical material. Using a step-by-step approach, it introduces mathematical material only as it is needed. Exercises range from routine computations and verifications to extensive programming projects and challenging proofs.