Some matrix nearness problems suggested by Tikhonov regularization
For practitioners solving small to moderate size ill-posed problems, this work offers new regularization techniques that can outperform existing standard methods.
The authors derive novel regularization methods for linear discrete ill-posed problems by considering matrix nearness problems related to Tikhonov regularization. These methods combine properties of Tikhonov regularization and TSVD, yielding approximate solutions of higher quality than either method alone.
The numerical solution of linear discrete ill-posed problems typically requires regularization, i.e., replacement of the available ill-conditioned problem by a nearby better conditioned one. The most popular regularization methods for problems of small to moderate size are Tikhonov regularization and truncated singular value decomposition (TSVD). By considering matrix nearness problems related to Tikhonov regularization, several novel regularization methods are derived. These methods share properties with both Tikhonov regularization and TSVD, and can give approximate solutions of higher quality than either one of these methods.