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A Parallel Divide and Conquer Algorithm for the Generalized Real Symmetric Definite Tridiagonal Eigenproblem

1992
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Release : 1992
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Book Synopsis A Parallel Divide and Conquer Algorithm for the Generalized Real Symmetric Definite Tridiagonal Eigenproblem by : Carlos F. Borges

Download or read book A Parallel Divide and Conquer Algorithm for the Generalized Real Symmetric Definite Tridiagonal Eigenproblem written by Carlos F. Borges. This book was released on 1992. Available in PDF, EPUB and Kindle. Book excerpt: We develop a parallel divide and conquer algorithm, by extension, for the generalized real symmetric definite tridiagonal eigenproblem. The algorithm employs techniques first proposed by Gu and Eisenstat to prevent loss of orthogonality in the computed eigenvectors for the modification algorithm. We examine numerical stability and adapt the insightful error analysis of Gu and Eisenstat to the arrow case. The algorithm incorporates an elegant zero finder with global monotone cubic convergence that has performed well in numerical experiments. A complete set of tested matlab routines implementing the algorithm is available on request from the authors.

Matrix Computations and Semiseparable Matrices

2008-12-15 Mathematics
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Release : 2008-12-15
Genre : Mathematics
Kind : eBook
Book Rating : 800/5 ( reviews)

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Book Synopsis Matrix Computations and Semiseparable Matrices by : Raf Vandebril

Download or read book Matrix Computations and Semiseparable Matrices written by Raf Vandebril. This book was released on 2008-12-15. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Numerical Linear Algebra

2011-06-01 Mathematics
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Release : 2011-06-01
Genre : Mathematics
Kind : eBook
Book Rating : 650/5 ( reviews)

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Book Synopsis Numerical Linear Algebra by : Lothar Reichel

Download or read book Numerical Linear Algebra written by Lothar Reichel. This book was released on 2011-06-01. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

A Coarse-grain Parallel Implementation of the Block Tridiagonal Divide and Conquer Algorithm for Symmetric Eigenproblems

2003
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Release : 2003
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Book Synopsis A Coarse-grain Parallel Implementation of the Block Tridiagonal Divide and Conquer Algorithm for Symmetric Eigenproblems by :

Download or read book A Coarse-grain Parallel Implementation of the Block Tridiagonal Divide and Conquer Algorithm for Symmetric Eigenproblems written by . This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt: Cuppen's divide and conquer technique for symmetric tridiagonal eigenproblems, along with Gu and Eisenstat's modification for improvement of the eigenvector computation, has yielded a stable, efficient, and widely-used algorithm. This algorithm has now been extended to a larger class of matrices, namely symmetric block tridiagonal eigenproblems. The Block Tridiagonal Divide and Conquer algorithm has shown several characteristics that make it suitable for a number of applications, such as the Self-Consistent-Field procedure in quantum chemistry. This thesis discusses the steps taken to implement a coarse-grain parallel version of the Block Tridiagonal Divide and Conquer algorithm, suitable for a parallel supercomputer or a cluster of machines. The parallel version relies on components of the ScaLAPACK parallel linear algebra library and follows the same model as the serial code, including the implementation of full deflation. A modest speedup (2 to 3) was achieved using a few processors (4 and 16). Increasing the number of processors from 4 to 16 produced only slightly better speedup. This implementation was not competitive with the standard ScaLAPACK symmetric eigenvalue routine.

Parallel Divide and Conquer Algorithms for the Symmetric Tridiagonal Eigenproblem

1994
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Release : 1994
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Book Synopsis Parallel Divide and Conquer Algorithms for the Symmetric Tridiagonal Eigenproblem by : Kevin Gates

Download or read book Parallel Divide and Conquer Algorithms for the Symmetric Tridiagonal Eigenproblem written by Kevin Gates. This book was released on 1994. Available in PDF, EPUB and Kindle. Book excerpt:

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