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Perturbation Analysis for the Matrix-Scaled Total Least Squares Problem
School of Science, Chongqing University of Posts and Telecommunications, Chongqing, China
School of Science, Chongqing University of Posts and Telecommunications, Chongqing, China
School of Science, Chongqing University of Posts and Telecommunications, Chongqing, China
- 1 School of Science, Chongqing University of Posts and Telecommunications, Chongqing, China
- 2 School of Science, Chongqing University of Posts and Telecommunications, Chongqing, China
- 3 School of Science, Chongqing University of Posts and Telecommunications, Chongqing, China
Advances in Pure Mathematics·Volume 11 (2021)·Pages 121–137·Published 5 February 2021·DOI10.4236/apm.2021.112008
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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.
KeywordsSingular Value DecompositionMatrix-Scaled Total Least SquaresTotal Least SquaresCondition Number
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