It is shown that the success of truncated singular value decomposition and Tikhonov regularization depends on a Picard condition. This is a continuation of the author’s earlier work [BIT 27, 534-553 (1987; Zbl 0633.65041)] where he showed that if there is a distinct gap in the singular value spectrum then the two methods are equivalent. In this paper the convergence of both methods is shown to depend primarily on the right-hand side. Perturbation bounds, behavior under the influence of errors and numerical examples are given.