On Tridiagonalizing and Diagonalizing Symmetric Matrices with Repeated Eigenvalues
We describe a divide-and-conquer tridiagonalization approach for matrices with repeated eigenvalues. Our algorithm hinges on the fact that, under easily constructively verifiable conditions, a symmet...
We describe a divide-and-conquer tridiagonalization approach for matrices with repeated eigenvalues. Our algorithm hinges on the fact that, under easily constructively verifiable conditions, a symmet...
On the Solution of a Nonlinear Matrix Equation Arising in Queueing Problems
By extending the cyclic reduction technique to infinite block matrices we devise a new algorithm for computing the solution $G_0 $ of the matrix equation $G = \Sigma _{i = 0}^{ + \infty } G^i A_i $ ar...
By extending the cyclic reduction technique to infinite block matrices we devise a new algorithm for computing the solution $G_0 $ of the matrix equation $G = \Sigma _{i = 0}^{ + \infty } G^i A_i $ ar...
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An Approximate Minimum Degree Ordering Algorithm
SIAM. J. Matrix Anal. & Appl. Volume 17, Issue 4, pp. 886-905 (October 1996)
Issue Date: October 1996
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Abstract. An approximate minimum degree (AMD), ordering algorithm for preordering a symmetric sparse matrix prior to numerical factorization is presented. We use techniques based on the quotient graph for matrix factorization that allow us to obtain computationally cheap bounds for the minimum degree. We show that these bounds are often equal to the actual degree. The resulting algorithm is typically much faster than previous minimum degree ordering algorithms and produces results that are comparable in quality with the best orderings from other minimum degree algorithms.
©1996 (Copyright) Society for Industrial and Applied Mathematics
| History: | Received 1994-12-19; accepted 1995-11-15 |
| Permalink: | http://dx.doi.org/10.1137/S0895479894278952 |
KEYWORDS and AMS
PUBLICATION DATA
0895-4798 (print)
1095-7162 (online)
SIAM