Jack J. Dongarra, Sven J. Hammarling, Danny C. Sorensen  Home/Search
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Abstract: In this paper we describe block algorithms for the reduction of a real symmetric matrix to tridiagonal form and for the reduction of a general real matrix to either bidiagonal or Hessenberg form using Householder transformations. The approach is to aggregate the transformations and to apply them in a blocked fashion, thus achieving algorithms that are rich in matrix-matrix operations. These reductions to condensed form typically comprise a preliminary step in the computation of eigenvalues or... (Update)
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...algorithms all use elementary Householder matrices, and have good vector performance. Block forms of these algorithms have been developed [17], but all require additional operations, and a significant proportion of the work must still be performed by Level 2 BLAS, so there is...
.... can be organized so that it involves level 3 BLAS operations, making use of the WY Householder aggregation technique described in x4.3 [53]. Extra arithmetic operations and storage are required, but greater efficiency is obtained through the use of block operations. Error...
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BibTeX entry: (Update)
Jack J. Dongarra, Sven J. Hammarling, and Danny C. Sorensen. Block reduction of matrices to condensed form for eigenvalue computations. Technical Report ANL/MCS--TM--99, Mathematics and Computer Science Division, Argonne National Laboratory, September 1987. http://citeseer.ist.psu.edu/dongarra87block.html More
@article{ dongarra89block,
author = "Jack J. Dongarra and Danny C. Sorensen and Sven J. Hammarling",
title = "Block Reduction of Matrices to Condensed Forms for Eigenvalue Computations",
journal = "J. Comp. Appl. Math.",
volume = "27",
number = "1--2",
pages = "215--227",
year = "1989",
url = "citeseer.ist.psu.edu/dongarra87block.html" }
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