Extrapolation and the method of regularization for generalized inverses

AbstractRichardson's “extrapolation to the limit” idea is applied to the method of regularization for approximating the generalized inverse of a linear operator in Hilbert space. Uniform error bounds for successive extrapolates are derived for the case of bounded linear operators with closed range. For bounded linear operators with arbitrary range, and for densely defined closed linear operators, pointwise error bounds are derived, assuming certain “smoothness” conditions on the data