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dqds WITH AGGRESSIE EARLY DEFLATION.
- Source :
-
SIAM Journal on Matrix Analysis & Applications . 2012, Vol. 33 Issue 1, p22-51. 30p. 2 Diagrams, 2 Charts, 6 Graphs. - Publication Year :
- 2012
-
Abstract
- The dqds algorithm computes all the singular values of an n x n bidiagonal matrix to high relative accuracy in O(n²) cost. Its efficient implementation is now available as a LAPACK subroutine and is the preferred algorithm for this purpose. In this paper we incorporate into dqds a technique called aggressive early deflation, which has been applied successfully to the Hessenberg QR algorithm. Extensive numerical experiments show that aggressive early deflation often reduces the dqds runtime significantly. In addition, our theoretical analysis suggests that with aggressive early deflation, the performance of dqds is largely independent of the shift strategy. We confirm through experiments that the zero-shift version is often as fast as the shifted version. We give a detailed error analysis to prove that with our proposed deflation strategy, dqds computes all the singular values to high relative accuracy. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08954798
- Volume :
- 33
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Matrix Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 79348645
- Full Text :
- https://doi.org/10.1137/110821330