Hello,
I am solving a constrained polynomial fitting problem in the least squares sense using a generalized RQ decomposition roughly the same way as LAPACK DGGLSE does it.
The problem I'm interested in is the following:
min ||Ax - C||
under the constraint
Bx = D
where C and D are matrices of right-hand sides.
I'm using a home-made C++ DGGLSE that allows to solve the problem above for several RHS from a single RQ decomposition (while DGGLSE only solves it for vectorial C and D). It's just a translation of LAPACK DGGLSE in C++ where I replace some LAPACK subroutines but the essential parts of DGGLSE are preserved.
As expected, I get a pretty ill-conditionned Vandermonde matrix from the minimization problem and when I try to get the general RQ decomposition using LAPACK DGGRQF, I notice that DGGRQF changes the rank of the matrix A. I suspect this is due to the very bad conditionning of the matrix.
Is there a way to specify a custom machine precision to LAPACK in order to avoid such issue ?
Thank you for your help, let me know if I'm not clear enough.
