Condition numbers of the multidimensional total least squares problems having more than one solution

Abstract

Recently, the condition numbers of the total least squares (TLS) problems having a unique solution have been studied at length in Zheng et al. (SIAM J. Matrix Anal. Appl. 38: 924–948, 2017). However, it is known that the TLS problem may have no solution, and even if an existing solution, it may not be unique. As a continuation of their work, in this paper, we investigate the condition numbers of the minimum Frobenius norm solution of the (multidimensional) TLS problem when having more than one solution. The tight and computable upper bound estimates of the normwise, mixed, and componentwise condition numbers are respectively derived. Some numerical experiments are performed to illustrate the tightness of these upper bounds.