Matrix Computations and Semiseparable Matrices
Title | Matrix Computations and Semiseparable Matrices PDF eBook |
Author | Raf Vandebril |
Publisher | JHU Press |
Pages | 594 |
Release | 2008-01-14 |
Genre | Mathematics |
ISBN | 0801896797 |
In recent years several new classes of matrices have been discovered and their structure exploited to design fast and accurate algorithms. In this new reference work, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi present the first comprehensive overview of the mathematical and numerical properties of the family's newest member: semiseparable matrices. The text is divided into three parts. The first provides some historical background and introduces concepts and definitions concerning structured rank matrices. The second offers some traditional methods for solving systems of equations involving the basic subclasses of these matrices. The third section discusses structured rank matrices in a broader context, presents algorithms for solving higher-order structured rank matrices, and examines hybrid variants such as block quasiseparable matrices. An accessible case study clearly demonstrates the general topic of each new concept discussed. Many of the routines featured are implemented in Matlab and can be downloaded from the Web for further exploration.
Matrix Computations and Semiseparable Matrices
Title | Matrix Computations and Semiseparable Matrices PDF eBook |
Author | Raf Vandebril |
Publisher | JHU Press |
Pages | 516 |
Release | 2008-12-15 |
Genre | Mathematics |
ISBN | 0801896800 |
The general properties and mathematical structures of semiseparable matrices were presented in volume 1 of Matrix Computations and Semiseparable Matrices. In volume 2, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi discuss the theory of structured eigenvalue and singular value computations for semiseparable matrices. These matrices have hidden properties that allow the development of efficient methods and algorithms to accurately compute the matrix eigenvalues. This thorough analysis of semiseparable matrices explains their theoretical underpinnings and contains a wealth of information on implementing them in practice. Many of the routines featured are coded in Matlab and can be downloaded from the Web for further exploration.
Matrix Computations
Title | Matrix Computations PDF eBook |
Author | Gene H. Golub |
Publisher | JHU Press |
Pages | 734 |
Release | 1996-10-15 |
Genre | Mathematics |
ISBN | 9780801854149 |
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.
Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications
Title | Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications PDF eBook |
Author | Michele Benzi |
Publisher | Springer |
Pages | 413 |
Release | 2017-01-24 |
Genre | Mathematics |
ISBN | 3319498878 |
Focusing on special matrices and matrices which are in some sense `near’ to structured matrices, this volume covers a broad range of topics of current interest in numerical linear algebra. Exploitation of these less obvious structural properties can be of great importance in the design of efficient numerical methods, for example algorithms for matrices with low-rank block structure, matrices with decay, and structured tensor computations. Applications range from quantum chemistry to queuing theory. Structured matrices arise frequently in applications. Examples include banded and sparse matrices, Toeplitz-type matrices, and matrices with semi-separable or quasi-separable structure, as well as Hamiltonian and symplectic matrices. The associated literature is enormous, and many efficient algorithms have been developed for solving problems involving such matrices. The text arose from a C.I.M.E. course held in Cetraro (Italy) in June 2015 which aimed to present this fast growing field to young researchers, exploiting the expertise of five leading lecturers with different theoretical and application perspectives.
Introduction to Matrix Computations
Title | Introduction to Matrix Computations PDF eBook |
Author | G. W. Stewart |
Publisher | Elsevier |
Pages | 457 |
Release | 1973-06-15 |
Genre | Mathematics |
ISBN | 0080926142 |
Numerical linear algebra is far too broad a subject to treat in a single introductory volume. Stewart has chosen to treat algorithms for solving linear systems, linear least squares problems, and eigenvalue problems involving matrices whose elements can all be contained in the high-speed storage of a computer. By way of theory, the author has chosen to discuss the theory of norms and perturbation theory for linear systems and for the algebraic eigenvalue problem. These choices exclude, among other things, the solution of large sparse linear systems by direct and iterative methods, linear programming, and the useful Perron-Frobenious theory and its extensions. However, a person who has fully mastered the material in this book should be well prepared for independent study in other areas of numerical linear algebra.
Handbook for Matrix Computations
Title | Handbook for Matrix Computations PDF eBook |
Author | Thomas F. Coleman |
Publisher | SIAM |
Pages | 271 |
Release | 1988-01-01 |
Genre | Mathematics |
ISBN | 9781611971040 |
Provides the user with a step-by-step introduction to Fortran 77, BLAS, LINPACK, and MATLAB. It is a reference that spans several levels of practical matrix computations with a strong emphasis on examples and "hands on" experience.
Matrix Computations
Title | Matrix Computations PDF eBook |
Author | Gene H. Golub |
Publisher | JHU Press |
Pages | 781 |
Release | 2013-02-15 |
Genre | Mathematics |
ISBN | 1421408597 |
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.