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### [Scalapack] complex pivoted qr factorisation

 ```Dear friends, the deep spike or more erratic behavior of the LINPACK QRCP is likely to happen when the scaled condition of A (cond(A with equilibrated columns)) exceeds 1/sqrt(machine precision). In other words, if scaled condition number is taken as a realistic sensitivity measure (and for the QRF it is), then LINPACK-style QRCP causes problems even if we could get half of the digits in the answer. Zvonimir and myself did not go into fixing this in the ScaLAPACK, we just assumed that ScaLAPACK developers will do that. (How far this bag can go, see an example in the attachment. That report contains some discussion related to our ACM TOMS paper on this.) I should point out here that the fix we provided for LAPACK is not the best we can -- a truly reliable implementation requires extra N scalars in the workspace, and that we could not afford because of backward compatibility. Best fix should get different name, because of this extra N locations in the workspace. Please let me know if you are interested in having this in (Sca)LAPACK. Best regards Zlatko On 20.10.2011. 15:26, James Demmel wrote: ``````On 10/20/11 6:01 AM, Sven Hammarling wrote: ``````Dear Jim, Unless I misunderstand (quite likely!), I think that Zlatko and Zvonimir showed a similar example in Figure 1 of LAWN 176 - it certainly has a deep spike. Once ScaLAPACK gets the LAPACK fix it will be interesting to see the result on David's example. Best wishes, Sven. ``````In that figure, the "true" answer is around macheps * norm(A), and R(i,i) drops down way below that. So everything is tiny. I think this is the only way you can get such completely out-of-order R(i,i), when everything is O(macheps*norm(A)) and so possibly totally losing all leading digits. In the example from David Wang below, R(3,3) is O(norm(A)) = O(1), and appears after R(2,2) = O(macheps), which can't be explained by the bug Zlatko and Zvonimir found: R(0,0) -0.707107 + 0i R(1,1) -0.707107 + 0i R(2,2) 8.16273e-17 + 0i R(3,3) -0.243173 + 0i R(4,4) 4.82605e-17 + 0i Jim ----- No virus found in this message. Checked by AVG - www.avg.com Version: 2012.0.1831 / Virus Database: 2092/4563 - Release Date: 10/20/11 `````` -------------- next part -------------- A non-text attachment was scrubbed... Name: sb.pdf Type: application/pdf Size: 1109485 bytes Desc: not available Url : http://lists.eecs.utk.edu/mailman/private/scalapack/attachments/20111020/50199983/sb-0001.pdf ```
 Current Thread [Scalapack] complex pivoted qr factorisation, David Wang [Scalapack] complex pivoted qr factorisation, James, Rodney [Scalapack] complex pivoted qr factorisation, James Demmel [Scalapack] complex pivoted qr factorisation, David Wang [Scalapack] complex pivoted qr factorisation, Sven Hammarling [Scalapack] complex pivoted qr factorisation, James Demmel [Scalapack] complex pivoted qr factorisation, Zlatko Drmac <= [Scalapack] complex pivoted qr factorisation, Sven Hammarling

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