On mixed and componentwise condition numbers for moore-penrose inverse and linear least squares problems

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Original languageEnglish
Pages (from-to)947-963
Journal / PublicationMathematics of Computation
Issue number258
Publication statusPublished - Apr 2007


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. ©2006 American Mathematical Society.

Research Area(s)

  • Componentwise analysis, Condition numbers, Least squares