Strange behavior in LSQR condition number estimate
Created by: michael-a-hansen
I am attempting to use LSQR to estimate the condition number of some matrices. I began testing my code on simple matrices for which I know the exact condition numbers. While I can successfully get K=1 for a scaled identity matrix, I get inaccurate condition numbers that depend heavily on the linear solve tolerance for matrices of any additional complexity. For instance, on a diagonal matrix with A_{i,i} = -i, I observe that the condition number estimate increases as I tighten solver tolerance, up to 33x the exact answer at machine precision tolerance. Is this behavior strange or am I wrong in my understanding that a converged linear solve with LSQR will correspond to a good estimate of the condition number?