论文标题
混合最小二乘最小二乘正方形的条件数量：重新审视
Condition numbers of the mixed least squares-total least squares problem: revisited
论文作者
论文摘要
提出了混合最小二乘最小二乘（MTL）溶液的一阶扰动估计的新闭合公式。它在数学上等同于Zheng和Yang（numer。Linear。Lineal代数Appl。2019; 26（4）：E2239）。使用此公式，常规和结构化的常规和结构化，得出了MTLS问题的混合和组合条件数量。还为经济存储和有效的计算提供了基于规范条件数量的扰动界限，并给出了混合和组件条件数量上限的紧凑形式。结果表明，在MTLS问题的问题中，TLS问题的条件数量和扰动结合是统一的。
A new closed formula for the first order perturbation estimate of the mixed least squares-total least squares (MTLS) solution is presented. It is mathematically equivalent to the one by Zheng and Yang(Numer. Linear Algebra Appl. 2019; 26(4):e2239). With this formula, general and structured normwise, mixed and componentwise condition numbers of the MTLS problem are derived. Perturbation bounds based on the normwise condition number, and compact forms for the upper bounds of mixed and componentwise condition numbers are also given in order for economic storage and efficient computation. It is shown that the condition numbers and perturbation bound of the TLS problem are unified in the ones of the MTLS problem.
