Approximation of generalized inverses by iterated regularization

Abstract

Abstract Approximations to the Moore-Penrose generalized inverse are obtained via iteration in the application of regularization. Uniform error bounds are obtained for linear operators with closed range. For operators with arbitrary range pointwise error estimates are derived assuming certain smoothness conditions on the data. The stability of the iteration is considered and error bounds are obtained for“noisy”data. ∗The work of this author was partially supported by NSF Grant MCS 76 24433 †This work performed while on leave at the University of Cincinnati ∗The work of this author was partially supported by NSF Grant MCS 76 24433 †This work performed while on leave at the University of Cincinnati Notes ∗The work of this author was partially supported by NSF Grant MCS 76 24433 †This work performed while on leave at the University of Cincinnati