Perturbation theory for the Eckart-Young-Mirsky theorem and the constrained total least squares problem

Golub et al. (Linear Algebra Appl. 88/89 (1987) 317–327), J.Demmel (SIAM J. Numer. Anal. 24 (1987) 199–206), generalized the Eckart-Young-Mirsky (EYM) theorem, which solves the problem of approximating a matrix by one of lower rank with only a specific rectangular subset of the matrix allowed to be changed. Based on their results, this paper presents perturbation analysis for the EYM theorem and the constrained total least squares problem (CTLS).