Mathematics for various disciplines On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems

2008-08-06 13:00 - 2008-08-06 14:00
Graduate School of Mathematical Sciences the University of Tokyo, Room #052
Yimin Wei (Fudan University, P.R. of China)
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 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.