Report10.21236/ADA302278
Modifying two-sided orthogonal decompositions: algorithms, implementation, and applications
Jesse L. Barlow,Peter A. Yoon +1 more
- 01 Jan 1996
- pp 190-190
TL;DR: This thesis proposes several algorithms for rank-one updates and downdates to these decompositions with strong stability properties and efficient implementations on high-performance computers.
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Abstract: : In this thesis we propose several algorithms for rank-one updates and downdates to these decompositions with strong stability properties and efficient implementations on high-performance computers. We seek algorithms which only require O(n2) operations per update or downdate unlike recomputing the two-sided orthogonal decomposition (TSOD) in O(n3). We also desire highly regular data movement inherited in these algorithms in order to implement these efficiently on the distributed memory MIMD multiprocessors. The algorithms are based upon 'chasing' strategies for updating and downdating procedures for orthogonal decompositions. (AN)
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Citations
Computing accurate eigensystems of scaled diagonally dominant matrices: LAPACK working note No. 7
J. Barlow,J. Demmel +1 more
- 01 Dec 1988
TL;DR: In this article, the singular values and eigenvalues of symmetric positive definite tridiagonal matrices are determined to high relative precision independent of their magnitudes, and there are algorithms to compute them this accurately.
164
An efficient rank detection procedure for modifying the ULV decomposition
Peter A. Yoon,Jesse L. Barlow +1 more
TL;DR: This paper proposes an efficient algorithm which almost always maintains rank-revealing structure of the decomposition after an update or downdate without standard condition estimation.
19
A modified Gram-Schmidt-based downdating technique for ULV decompositions with applications to recursive TLS problems
TL;DR: The ULV decomposition is an important member of a class of rank-revealing two-sided orthogonal decompositions used to approximate the singular value decomposition (SVD) as mentioned in this paper.
16
•Posted Content
Low-rank approximation in the Frobenius norm by column and row subset selection
Alice Cortinovis,Daniel Kressner +1 more
TL;DR: In this paper, a column subset selection algorithm with an error bound that stays within a factor (k + 1) of the best rank-k approximation error in the Frobenius norm is presented.
14
Modification and Maintenance of ULV Decompositions
Jesse L. Barlow
- 01 Jan 2002
TL;DR: The ULV decomposition is an important member of a class of rank-revealing two-sided orthogonal decompositions used to approximate the singular value decomposition (SVD).
11
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