An analysis of the mixed least squares-total least squares problems

Abstract

In this paper, we first get further  consideration of the first order perturbation with normwise condition number of the MTLS problem. For easy estimation, we show a lower bound for the normwise condition number which is proved to be optimal. In order to overcome the problems encountered in calculating the normwise condition number, we give an upper bound for computing more effectively and nonstandard and unusual perturbation bounds for the MTLS problem. Both of the two types of the perturbation bounds can enjoy storage and computational advantages. For getting more insight into the sensitivity of the MTLS technique with respect to perturbations in all data, we analyze the corrections applied by MTLS to the data in $Ax\approx b$ to make the set compatible and indicate how closely the data $A, b$ fit the so-called general errors-in-variables model. On how to estimate the conditioning of the MTLS problem more effectively, we propose statistical algorithms by taking advantage of the superiority of small sample statistical condition estimation (SCE) techniques.