On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems
On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems
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DOI：
10.1090/s0025-5718-06-01913-2
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发表时间：
2006-11
期刊：
影响因子：
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通讯作者：
F. Cucker;H. Diao;Yimin Wei-
中科院分区：
文献类型：
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作者：
F. Cucker;H. Diao;Yimin Wei-
经典条件数是范数的：它们使用某些范数来测量输入扰动和输出误差的大小。为了考虑到每个数据分量的相对性，特别是可能的数据稀疏性，已经越来越多地考虑分量条件数。它们主要有两种：混合型和组件型。在本文中，我们给出了可根据数据计算的显式表达式，用于计算 Moore-Penrose 逆矩阵以及计算线性最小二乘问题的解和留数的混合条件数和分量条件数。在这两种情况下，数据矩阵都具有完整的列（行）等级。
Classical condition numbers are normwise: they measure the size of both input perturbations and output errors using some norms. To take into account the relative of each data component, and, in particular, a possible data sparseness, componentwise condition numbers have been increasingly considered. These are mostly of two kinds: mixed and componentwise. In this paper, we give explicit expressions, computable from the data, for the mixed and componentwise condition numbers for the computation of the Moore-Penrose inverse as well as for the computation of solutions and residues of linear least squares problems. In both cases the data matrices have full column (row) rank.