A note on the condition number of the scaled total least squares problem
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In this paper, we show that the normwise condition number of the scaled total least squares problem can be transformed into a new and compact form. Considering the relationship between the scaled total least squares problem and the total least squares problem, we obtain something new on the normwise condition number of the total least squares problem. The new forms of the normwise condition number are of particular interest in the following two aspects. Firstly, it is easy to use for the practitioners from applied disciplines. Secondly, the new forms enjoy great computational efficiency and require very little storage space compared with its original forms. Numerical examples are given to illustrate the results.
KeywordsThe scaled total least squares problem Normwise condition number Compact form Condition number estimation
Mathematics Subject Classification65F35 15A63 15A06
The authors are grateful to the anonymous referees and the Editor for their detailed and helpful comments that led to a substantial improvement to the paper.
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