This paper is devoted to condition numbers of the total least squares problem with linear equality constraint (TLSE). With novel limit techniques, closed formulae for normwise, mixed and componentwise condition numbers of the TLSE problem are derived. Computable expressions and upper bounds for these condition numbers are also given to avoid the costly Kronecker product-based operations. The results unify the ones for the TLS problem. For TLSE problems with equilibratory input data, numerical experiments illustrate that normwise condition number-based estimate is sharp to evaluate the forward error of the solution, while for sparse and badly scaled matrices, mixed and componentwise condition numbers-based estimates are much tighter.

翻译：本文专门论述线性平等限制(TLSE)下所有最不平方问题的条件号。 有了新的限制技术, 就可以得出关于TLSE问题规范、 混合和组成部分条件号的封闭公式。 这些条件号的可计算表达式和上限也是为了避免昂贵的Kronecker产品操作。 结果将 TLS 问题的条件号统一起来。 关于 TLS 问题, 数字实验表明, 常规性基于数字的估计数对于评估解决办法的远端错误来说是敏锐的, 而对于稀有和过大的矩阵, 混合和组成部分性基于条件的数字估计数则要紧得多。