On Mixed and Componentwise Condition Numbers for Moore-Penrose Inverse and Linear Least Squares Problems
by
Yi-Min Wei
School of Mathematical SciencesFudan University
Shanghai, 200433, P.R. China
Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University)
Ministry of Education, Shanghai, 200433, P.R. of China
Email: ymwei@fudan.edu.cn
Abstract : 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 talk,
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.
Keywords: linear least squares, condition numbers
AMS subject classi¯cations(1991): 15A18, 65F20, 65F25, 65F50.
Keywords: linear least squares, condition numbers
AMS subject classi¯cations(1991): 15A18, 65F20, 65F25, 65F50.