论文标题
对线性相等性约束的多维总和最小二乘问题的条件数量的贡献
A contribution to condition numbers of the multidimensional total least squares problem with linear equality constraint
论文作者
论文摘要
本文致力于与线性平等约束（TLSE）的多维总和正方形问题的条件。基于不变子空间的扰动理论，事实证明，TLSE问题等同于在极限意义上的多维无约束权衡总和最小二乘问题。使用限制技术，给出了基于Kronecker-rodotuct的公式，用于规范，混合和组件条件的最小frobenius Norm TLSE解决方案的条件数量。提供这些条件数字的紧凑上限以降低存储和计算成本。这些条件数的所有表达式和上限都统一了单维tlse问题和多维总正方形问题的表达式和界限。进行一些数值实验以说明我们的结果。
This paper is devoted to condition numbers of the multidimensional total least squares problem with linear equality constraint (TLSE). Based on the perturbation theory of invariant subspace, the TLSE problem is proved to be equivalent to a multidimensional unconstrained weighed total least squares problem in the limit sense. With a limit technique, Kronecker-product-based formulae for normwise, mixed and componentwise condition numbers of the minimum Frobenius norm TLSE solution are given. Compact upper bounds of these condition numbers are provided to reduce the storage and computation cost. All expressions and upper bounds of these condition numbers unify the ones for the single-dimensional TLSE problem and multidimensional total least squares problem. Some numerical experiments are performed to illustrate our results.
