Some results on condition numbers of the scaled total least squares problem

Under the Golub–Van Loan condition for the existence and uniqueness of the scaled total least squares (STLS) solution, a first order perturbation estimate for the STLS solution and upper bounds for condition numbers of a STLS problem have been derived by Zhou et al. recently. In this paper, a different perturbation analysis approach for the STLS solution is presented. The analyticity of the solution to the perturbed STLS problem is explored and a new expression for the first order perturbation estimate is derived. Based on this perturbation estimate, for some STLS problems with linear structure we further study the structured condition numbers and derive estimates for them. Numerical experiments show that the structured condition numbers can be markedly less than their unstructured counterparts.