#### Volume 55, pp. 618-626, 2022.

## A contribution to the conditioning of the mixed least-squares scaled total least-squares problem

Lingsheng Meng

### Abstract

A new closed formula for first-order perturbation estimates for the solution of the mixed least-squares scaled total least-squares (MLSSTLS) problem is presented. It is mathematically equivalent to the one by [Zhang and Wang, Numer. Algorithms, 89 (2022), pp. 1223–1246]. With this formula, new closed formulas for the relative normwise, mixed, and componentwise condition numbers of the MLSSTLS problem are derived. Compact forms and upper bounds for the relative normwise condition number are also given in order to obtain economic storage and efficient computations.

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### Key words

mixed least-squares scaled total least-squares, condition numbers, mixed least-squares total least-squares

### AMS subject classifications

65F20, 65F35

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