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| Author | : Raf Vandebril |
| Publisher | : JHU Press |
| Total Pages | : 594 |
| Release | : 2008-01-14 |
| Genre | : Mathematics |
| ISBN | : 0801896797 |
Download Matrix Computations and Semiseparable Matrices Book in PDF, ePub and Kindle
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.
| Author | : Raf Vandebril |
| Publisher | : JHU Press |
| Total Pages | : 516 |
| Release | : 2008-12-15 |
| Genre | : Mathematics |
| ISBN | : 0801896800 |
Download Matrix Computations and Semiseparable Matrices Book in PDF, ePub and Kindle
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.
| Author | : Gene H. Golub |
| Publisher | : JHU Press |
| Total Pages | : 734 |
| Release | : 1996-10-15 |
| Genre | : Mathematics |
| ISBN | : 9780801854149 |
Download Matrix Computations Book in PDF, ePub and Kindle
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 | : Thomas F. Coleman |
| Publisher | : SIAM |
| Total Pages | : 271 |
| Release | : 1988-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781611971040 |
Download Handbook for Matrix Computations Book in PDF, ePub and Kindle
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.
| Author | : Michele Benzi |
| Publisher | : Springer |
| Total Pages | : 406 |
| Release | : 2017-01-24 |
| Genre | : Mathematics |
| ISBN | : 3319498878 |
Download Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications Book in PDF, ePub and Kindle
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.
| Author | : Gene H. Golub |
| Publisher | : JHU Press |
| Total Pages | : 781 |
| Release | : 2013-02-15 |
| Genre | : Mathematics |
| ISBN | : 1421408597 |
Download Matrix Computations Book in PDF, ePub and Kindle
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.
| Author | : James R. Bunch |
| Publisher | : Academic Press |
| Total Pages | : 468 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483263401 |
Download Sparse Matrix Computations Book in PDF, ePub and Kindle
Sparse Matrix Computations is a collection of papers presented at the 1975 Symposium by the same title, held at Argonne National Laboratory. This book is composed of six parts encompassing 27 chapters that contain contributions in several areas of matrix computations and some of the most potential research in numerical linear algebra. The papers are organized into general categories that deal, respectively, with sparse elimination, sparse eigenvalue calculations, optimization, mathematical software for sparse matrix computations, partial differential equations, and applications involving sparse matrix technology. This text presents research on applied numerical analysis but with considerable influence from computer science. In particular, most of the papers deal with the design, analysis, implementation, and application of computer algorithms. Such an emphasis includes the establishment of space and time complexity bounds and to understand the algorithms and the computing environment. This book will prove useful to mathematicians and computer scientists.
| Author | : John Rischard Rice |
| Publisher | : McGraw-Hill Companies |
| Total Pages | : 280 |
| Release | : 1981 |
| Genre | : Computers |
| ISBN | : |
Download Matrix Computations and Mathematical Software Book in PDF, ePub and Kindle
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 | : Åke Björck |
| Publisher | : Springer |
| Total Pages | : 800 |
| Release | : 2014-10-07 |
| Genre | : Mathematics |
| ISBN | : 3319050893 |
Download Numerical Methods in Matrix Computations Book in PDF, ePub and Kindle
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.
| Author | : Joel W. Robbin |
| Publisher | : CRC Press |
| Total Pages | : 560 |
| Release | : 2018-10-08 |
| Genre | : Mathematics |
| ISBN | : 1439864772 |
Download Matrix Algebra Using MINimal MATlab Book in PDF, ePub and Kindle
The strength of this textbook lies in the careful exposition of mathematical thinking, basic set-theoretic notions, and proof techniques combined with contemporary numerical methods used throughout the book. A basic version of computer programs compatible with the widely used program MatLab, and exercises are provided on a disk included with the book.Warmup * Matrix Operations * Invertible Matrices * Subspaces * Rank and Dimension * Geometry * Determinants-I * Diagonalization * Differential Equations * Hermitian Matrices * Triangular Matrices * Unitary Matrices * Block Diagonalization * Jordan Normal Form * Determinants-II * Proofs * Mathematical Induction†* Summary of MINIMAT * Answers * MINIMAT Tutorial (PC Version)
