An algorithm for solving rank-deficient scaled total least square problems

The scaled total least square (STLS) problem, introduced by B.D. Rao in 1997, unifies both the total least square (TLS) and the least square (LS) problems. The STLS problems can be solved by the singular value decomposition (SVD). In this paper, we give a rank-revealing two-sided orthogonal decomposition method for solving the STLS problem. An error analysis is presented. Our numerical experiments show that this algorithm computes the STLS solution as good as the SVD method with less computation.