[Lapack] Proposed interfaces for extra-precise refinement.
From: Xiaoye S. Li
Date: Tue, 18 Apr 2006 12:46:14 -0700
* 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?
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
2) The actual workspace size. If we remove the
cautious scaling from the condition number
estimator, we need either N or 2*N less