Polynomial And Matrix Computations
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Author |
: Dario Bini |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 433 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461202653 |
ISBN-13 |
: 1461202655 |
Rating |
: 4/5 (53 Downloads) |
Synopsis Polynomial and Matrix Computations by : Dario Bini
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 |
Total Pages |
: 170 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461251187 |
ISBN-13 |
: 1461251184 |
Rating |
: 4/5 (87 Downloads) |
Synopsis Error-Free Polynomial Matrix Computations by : E.V. Krishnamurthy
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 |
: |
Total Pages |
: |
Release |
: 1994 |
ISBN-10 |
: OCLC:715642154 |
ISBN-13 |
: |
Rating |
: 4/5 (54 Downloads) |
Synopsis Polynomial and Matrix Computations by : Dario Bini
Author |
: Victor Y. Pan |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 299 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461201298 |
ISBN-13 |
: 1461201292 |
Rating |
: 4/5 (98 Downloads) |
Synopsis Structured Matrices and Polynomials by : Victor Y. Pan
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 |
: |
Total Pages |
: 476 |
Release |
: 1983 |
ISBN-10 |
: 0946536058 |
ISBN-13 |
: 9780946536054 |
Rating |
: 4/5 (58 Downloads) |
Synopsis Matrix Computations by : Gene Howard Golub
Author |
: Dingyü Xue |
Publisher |
: Walter de Gruyter GmbH & Co KG |
Total Pages |
: 301 |
Release |
: 2020-03-23 |
ISBN-10 |
: 9783110666991 |
ISBN-13 |
: 3110666995 |
Rating |
: 4/5 (91 Downloads) |
Synopsis Linear Algebra and Matrix Computations with MATLAB® by : Dingyü Xue
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.
Author |
: Gene H. Golub |
Publisher |
: JHU Press |
Total Pages |
: 734 |
Release |
: 1996-10-15 |
ISBN-10 |
: 0801854148 |
ISBN-13 |
: 9780801854149 |
Rating |
: 4/5 (48 Downloads) |
Synopsis Matrix Computations by : Gene H. Golub
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 |
: Hans J. Stetter |
Publisher |
: SIAM |
Total Pages |
: 475 |
Release |
: 2004-05-01 |
ISBN-10 |
: 9780898715576 |
ISBN-13 |
: 0898715571 |
Rating |
: 4/5 (76 Downloads) |
Synopsis Numerical Polynomial Algebra by : Hans J. Stetter
This book is the first comprehensive treatment of numerical polynomial algebra, an area which so far has received little attention.
Author |
: Alicia Dickenstein |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 433 |
Release |
: 2005-04-27 |
ISBN-10 |
: 9783540243267 |
ISBN-13 |
: 3540243267 |
Rating |
: 4/5 (67 Downloads) |
Synopsis Solving Polynomial Equations by : Alicia Dickenstein
This book provides a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems. It presents the state of the art in several symbolic, numeric, and symbolic-numeric techniques, including effective and algorithmic methods in algebraic geometry and computational algebra, complexity issues, and applications ranging from statistics and geometric modelling to robotics and vision. Graduate students, as well as researchers in related areas, will find an excellent introduction to currently interesting topics. These cover Groebner and border bases, multivariate resultants, residues, primary decomposition, multivariate polynomial factorization, homotopy continuation, complexity issues, and their applications.
Author |
: Gene H. Golub |
Publisher |
: Princeton University Press |
Total Pages |
: 376 |
Release |
: 2009-12-07 |
ISBN-10 |
: 9781400833887 |
ISBN-13 |
: 1400833884 |
Rating |
: 4/5 (87 Downloads) |
Synopsis Matrices, Moments and Quadrature with Applications by : Gene H. Golub
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.