NCKU Math colloquium
DATE	2009-04-23　16:10-17:00
PLACE	數學系三樓會議室
SPEAKER	魏益民 教授（上海復旦大學）
TITLE	On mixed and componentwise condition numbers for linear least squares and total least squares
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 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 and total least squares problems. In both cases the datamatrices have full column (row) rank.