[petsc-users] Parallel QR decomposition

[David Sommer]

Hi,

sorry i haven't answered in a while.
>>  i was wondering if there is an implementation of parallel qr
decomposition in PETSc.
>  For what purpose do you need a QR? We may have suggestions if we know
how you want to use it.
I found an interesting algorithm for radial basis function interpolation.
It mitigates the ill-conditioning that arises from making radial basis
functions increasingly flat. The paper can be found at
https://amath.colorado.edu/faculty/fornberg/Docs/SISCmanuscript.pdf
The algorithm defines a Matrix C that is rectangular (more columns than
rows). Then a QR Decomposition of C is computed. It looks like this:
C = Q [R1 R2]
with R1 being rectangular and R2 being stacked on it horizontally. What i
want to compute in the end is:
R_1^{-1} R_2
Which isn't that hard to compute once R is known, as this is just backward
substitution. Anyway i still need to do a full QR decomposition (Even
though i don't actually need Q, it would be easy to calculate from R, so i
don't think there is any shortcut to Q, except that i don't have to store
Q).
What i was thinking of as a possible solution is to parallelize Givens
rotations by leveraging the fact that it only has local row-wise data
dependencies in each step.

Best regards

David Sommer
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