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[Lapack] Proposed interfaces for extra-precise refinement.

*       PARAMS(ITHRESH_PARAM = 3) : Total number of residual computations
*            allowed for refinement.
*         Default: 10 for double-precision, 5 for single-precision
*         Aggressive: Set to 100 for our "aggresive" settings.
*

I think we have decided to remove single-precision (or working-precision)
refinement.  So the default should be 10 always?

For least squares refinement, it seems we will need two separate
ERR_BNDS arrays, one for X, another for residual R.

Also, there are several reciprocal condition numbers floating around:
RCOND of A
RCOND of the augmented system [ I   A ; A'  0]
RCOND of X
RCOND of R

Shall we return all of them?


Sherry


Jason Riedy wrote:

Appended are the proposed interfaces for extra-precise
refinement in single precision.  Other precisions and
matrix types are similar.  The interfaces are, alas, 
complicated.  Comments appreciated.

 SGESVXX : Expert driver that factors, solves, and refines.

 SGERFSX : Refinement routine itself.

Still in flux:
 1) How to query for the workspace size.  The complex 
    version has integer, real, and complex workspace;
    adding three LWORK-like parameters feels a bit
    strange.

 2) The actual workspace size.  If we remove the
    cautious scaling from the condition number 
    estimator, we need either N or 2*N less
    workspace.

Jason

 


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