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


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.

Lecture Slide