In this paper, by exploiting the special structure of the least squares problem and working on the problem directly, a numerically stable QR decomposition based algorithm is presented for the problem.

Mathematics of Computation, Vol. 71, No. 240 (Oct., 2002), pp. 1473-1496 (24 pages) This paper shows that for unitary Hessenberg matrices the QR algorithm, with (an exceptional initial-value ...