Gohberg, I. and Koltracht, I. (1993) Mixed, Componentwise and Structured Condition Numbers. SIAM Journal on Matrix Analysis and Applications, 14, 688-704.
https://doi.org/10.1137/0614049

has been cited by the following article:

• TITLE: Perturbation Analysis for the Matrix-Scaled Total Least Squares Problem

  AUTHORS: Qun Wang, Longyan Li, Pingping Zhang

  KEYWORDS: Singular Value Decomposition, Matrix-Scaled Total Least Squares, Total Least Squares, Condition Number

  JOURNAL NAME: Advances in Pure Mathematics, Vol.11 No.2, February 8, 2021

  ABSTRACT: In this paper, we extend matrix scaled total least squares (MSTLS) problem with a single right-hand side to the case of multiple right-hand sides. Firstly, under some mild conditions, this paper gives an explicit expression of the minimum norm solution of MSTLS problem with multiple right-hand sides. Then, we present the Kronecker-product-based formulae for the normwise, mixed and componentwise condition numbers of the MSTLS problem. For easy estimation, we also exhibit Kronecker-product-free upper bounds for these condition numbers. All these results can reduce to those of the total least squares (TLS) problem which were given by Zheng et al. Finally, two numerical experiments are performed to illustrate our results.