Mixed and component wise condition numbers for weighted Moore-Penrose inverse and weighted least squares problems

Condition numbers play an important role in numerical analysis. Classical condition numbers are norm-wise: they measure both input perturbations and output errors with norms. To take into account the relative scaling of data components or a possible sparseness, component-wise condition numbers have been increasingly considered. In this paper, we give explicit expressions for the mixed and component-wise condition numbers for the weighted Moore-Penrose inverse of a matrix A, as well as for the solution and residue of a weighted linear least squares problem ||W 1 2 (Ax-b) ||2 = minv2Rn ||W 1 2 (Av-b) ||2, where the matrix A with full column rank. .