Name
Abstract | ||
|---|---|---|
The dqds algorithm computes all the singular values of an $n \times n$ bidiagonal matrix to high relative accuracy in $O(n^2)$ 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. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1137/110821330 | SIAM J. Matrix Analysis Applications |
Keywords | Field | DocType |
preferred algorithm,detailed error analysis,proposed deflation strategy,high relative accuracy,aggressive early deflation,shift strategy,dqds algorithm,theoretical analysis,singular value,hessenberg qr algorithm,singular values,bidiagonal matrix,matrix theory | Mathematical optimization,Singular value,Subroutine,Matrix (mathematics),Bidiagonal matrix,Deflation,Mathematics,QR algorithm | Journal |
Volume | Issue | ISSN |
33 | 1 | 0895-4798 |
Citations | PageRank | References |
3 | 0.45 | 11 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yuji Nakatsukasa | 1 | 97 | 17.74 |
| Kensuke Aishima | 2 | 13 | 4.05 |
| Ichitaro Yamazaki | 3 | 174 | 25.27 |