Dear Sir:

I need solve a large sparse unsymmetrical overdetermined systems, Ax=B, where A is m by n, and m>n. A is a full rank matrix. But it is possible that some equations are inconsistent. For example, x1+x2=1, and x1+x2=2 are inconsistent. I need to detect the inconsistency in Ax=B first, if it exists, then needs not solve the equation; If it does not exist, solve the system.

I will detect the inconsistent in this way: equation Ax=B can be wrote as Rx= QTB, where rank of R is k. If the last (k+1), (k+2)… (m-k) of QTB are not equal to 0, then inconsistency exists. Otherwise, inconsistency does not exist.

I have two questions

1. Is my method of detect the insistences is correct? (obtain R by calling DGEQRF and obtain QtB by calling DORMQR ). Or other more effective routine can be used?

2. If QR factorization is sparse QR factorization in DGEQRF? If yes, any reference about it?

Thanks