Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank. (English) Zbl 0699.65029
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.
Reviewer: R.P.Tewarson
MSC:
65F20 | Numerical solutions to overdetermined systems, pseudoinverses |
65F35 | Numerical computation of matrix norms, conditioning, scaling |