ScaLAPACK Archives

[Scalapack] complex pivoted qr factorisation

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,

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 
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


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