### On Mixed and Componentwise
Condition Numbers for Moore-Penrose Inverse and Linear Least Squares
Problems

by

**
Yi-Min Wei**

School of Mathematical Sciences

Fudan 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.