I still seem to get signficant differences on the norm differences of Householder QR and QR via Cholesky trick. our stock in-core QR seems to be comfortable populating some R values (and therefore Q columns) with values as small as 1e-16, whereas Cholesky computation for L seems to set these things to 0. Norms on Q in this case differ more than trivially.
Are we sure we cannot decrease sensitivity of Cholesky decomposition to small values? I have manipulated the limit there that controls the decision for positive-definite-ness but I am not sure i understand algorithm well enough to do a meaningful sensitivity reduction.
