Generalized singular value decomposition with iterated Tikhonov regularization

[摘要] Linear discrete ill-posed problems arise in many areas of science and engineering. Their solutions are very sensitive to perturbations in the data. Regularization methods try to reduce the sensitivity by replacing the given problem by a nearby one, whose solution is less affected by perturbations. This paper describes how generalized singular value decomposition can be combined with iterated Tikhonov regularization and illustrates that the method so obtained determines approximate solutions of higher quality than the more commonly used approach of pairing generalized singular value decomposition with (standard) Tikhonov regularization. The regularization parameter is determined with the aid of the discrepancy principle. This requires the application of a zero-finder. Several zero-finders are compared. (C) 2019 Elsevier B.V. All rights reserved.

[发布日期] 2020-08-01

[效力级别]  Proceedings Paper

[关键词] Ill-posed problem;Iterated Tikhonov;GSVD;Zero-finder