论文标题
在最小二乘问题的条件下，线性平等约束
On condition numbers of the 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）的总和正方形问题的条件。使用新颖的极限技术，得出了针对标准的封闭公式，TLSE问题的混合和组件条件数量。还提供了这些条件数字的可计算表达式和上限，以避免基于Kronecker产品的昂贵操作。结果统一了TLS问题的结果。对于具有平衡输入数据的TLSE问题，数值实验表明，基于条件数的估计值是尖锐的，可以评估解决方案的正向误差，而对于稀疏且规模不佳的矩阵，混合条件和基于Componention的估计值的估计值更加严格。
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.
