A note on the scaled total least squares problem

In this note, we present two results on the scaled total least squares problem. First, we discuss the relation between the scaled total least squares and the least squares problems. We derive an upper bound for the difference between the scaled total least squares solution and the least squares solution and establish a quantitative relation between the scaled total least squares residual and the least squares residual. Second, we give a perturbation analysis of the scaled total least squares problem. Numerical experiments in comparing our results with existing results are demonstrated.