Matrix Computations

Matrix Computations PDF Author: Gene H. Golub
Publisher: JHU Press
ISBN: 1421408597
Category : Mathematics
Languages : en
Pages : 781

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Book Description
A comprehensive treatment of numerical linear algebra from the standpoint of both theory and practice. The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this book to be an indispensible tool. This revision is a cover-to-cover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on • fast transforms • parallel LU • discrete Poisson solvers • pseudospectra • structured linear equation problems • structured eigenvalue problems • large-scale SVD methods • polynomial eigenvalue problems Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literature—everything needed to become a matrix-savvy developer of numerical methods and software. The second most cited math book of 2012 according to MathSciNet, the book has placed in the top 10 for since 2005.

Matrix Computations

Matrix Computations PDF Author: Gene H. Golub
Publisher: JHU Press
ISBN: 1421408597
Category : Mathematics
Languages : en
Pages : 781

Get Book Here

Book Description
A comprehensive treatment of numerical linear algebra from the standpoint of both theory and practice. The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this book to be an indispensible tool. This revision is a cover-to-cover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on • fast transforms • parallel LU • discrete Poisson solvers • pseudospectra • structured linear equation problems • structured eigenvalue problems • large-scale SVD methods • polynomial eigenvalue problems Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literature—everything needed to become a matrix-savvy developer of numerical methods and software. The second most cited math book of 2012 according to MathSciNet, the book has placed in the top 10 for since 2005.

Numerical Treatment of Eigenvalue Problems Vol. 5 / Numerische Behandlung von Eigenwertaufgaben Band 5

Numerical Treatment of Eigenvalue Problems Vol. 5 / Numerische Behandlung von Eigenwertaufgaben Band 5 PDF Author: ALBRECHT
Publisher: Birkhäuser
ISBN: 3034863322
Category : Science
Languages : en
Pages : 248

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Book Description


Numerical Methods in Matrix Computations

Numerical Methods in Matrix Computations PDF Author: Åke Björck
Publisher: Springer
ISBN: 3319050893
Category : Mathematics
Languages : en
Pages : 812

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Book Description
Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work.

Iterative Methods for Toeplitz Systems

Iterative Methods for Toeplitz Systems PDF Author: Michael K. Ng
Publisher: Numerical Mathematics and Scie
ISBN: 9780198504207
Category : Computers
Languages : en
Pages : 370

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Book Description
Toeplitz and Toeplitz-related systems arise in a variety of applications in mathematics and engineering, especially in signal and image processing.

Polynomial and Matrix Computations

Polynomial and Matrix Computations PDF Author: Dario Bini
Publisher: Springer Science & Business Media
ISBN: 1461202655
Category : Computers
Languages : en
Pages : 433

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Book Description
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.

Toeplitz and Circulant Matrices

Toeplitz and Circulant Matrices PDF Author: Robert M. Gray
Publisher: Now Publishers Inc
ISBN: 1933019239
Category : Computers
Languages : en
Pages : 105

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Book Description
The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hope of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject. By limiting the generality of the matrices considered, the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes. The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hope of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject. By limiting the generality of the matrices considered, the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes.

Fast Reliable Algorithms for Matrices with Structure

Fast Reliable Algorithms for Matrices with Structure PDF Author: T. Kailath
Publisher: SIAM
ISBN: 0898714311
Category : Computers
Languages : en
Pages : 350

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Book Description
This book deals with the combined issues of speed and numerical reliability in algorithm development.

SIAM Journal on Matrix Analysis and Applications

SIAM Journal on Matrix Analysis and Applications PDF Author:
Publisher:
ISBN:
Category : Electronic journals
Languages : en
Pages : 660

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Book Description
Contains research articles on linear algebra with emphasis on applications and numerical procedures. These applications include such areas as Markov chains, networks, signal processing, systems and control theory, mathematical programming, economic and biological modeling, and statistics and operations research.

Solving Differential Equations by Multistep Initial and Boundary Value Methods

Solving Differential Equations by Multistep Initial and Boundary Value Methods PDF Author: L Brugnano
Publisher: CRC Press
ISBN: 9789056991074
Category : Mathematics
Languages : en
Pages : 438

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Book Description
The numerical approximation of solutions of differential equations has been, and continues to be, one of the principal concerns of numerical analysis and is an active area of research. The new generation of parallel computers have provoked a reconsideration of numerical methods. This book aims to generalize classical multistep methods for both initial and boundary value problems; to present a self-contained theory which embraces and generalizes the classical Dahlquist theory; to treat nonclassical problems, such as Hamiltonian problems and the mesh selection; and to select appropriate methods for a general purpose software capable of solving a wide range of problems efficiently, even on parallel computers.

IBM Journal of Research and Development

IBM Journal of Research and Development PDF Author:
Publisher:
ISBN:
Category : Electrical engineering
Languages : en
Pages : 610

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Book Description