This paper considers the mixed least squares-scaled total least squares (MLSSTLS) problem which unifies the mixed least squares-total least squares (MTLS) problem and the scaled total least squares (STLS) problem. Firstly, we present the explicit expression of the MLSSTLS solution under some conditions. Then, the perturbation analysis and condition numbers of the MLSSTLS solution are obtained. These results can reduce to some corresponding published results of the MTLS problem and the STLS problem, respectively. Finally, numerical experiments are given to illustrate our results.

中文翻译：

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混合最小二乘尺度总最小二乘问题的扰动分析和条件数

本文考虑了混合最小二乘缩放总最小二乘 (MLSSTLS) 问题，它统一了混合最小二乘总最小二乘 (MTLS) 问题和缩放总最小二乘 (STLS) 问题。首先，我们给出了在某些条件下 MLSSLTLS 解的显式表达。然后，得到了MLSSTLS解的扰动分析和条件数。这些结果可以分别简化为 MTLS 问题和 STLS 问题的一些相应的已发表结果。最后，给出了数值实验来说明我们的结果。