Bounds for the least squares distance using scaled total least squares (Q1597707)

The authors analyze fundamentals of the scaled total least squares problem. They present a theoretical analysis of the relationship between the sizes of least squares and scaled least squares corrections in terms of the real positive corrections restricted parameter. New upper and lower bounds on the least squares distance in terms of the scaled total least squares distances are given. They are compared to existing bounds and the tightness of the new bounds is examined. The obtained results can be applied to the analysis of iterative methods which minimize the residual norm. The generalized minimum residual method is used to illustrate the theoretical results.