Iterative implementation of the adaptive regularization yields optimality
Abbreviated Journal Title
Sci. China Ser. A-Math.
ill-posed problems; non-stationary iterated adaptive regularization; optimality; ILL-POSED PROBLEMS; TIKHONOV REGULARIZATION; Mathematics, Applied; Mathematics
The adaptive regularization method is first proposed by Ryzhikov et al. for the deconvolution in elimination of multiples. This method is stronger than the Tikhonov regularization in the sense that it is adaptive, i.e. it eliminates the small eigenvalues of the adjoint operator when it is nearly singular. We will show in this paper that the adaptive regularization can be implemented iterately. Some properties of the proposed non-stationary iterated adaptive regularization method are analyzed. The rate of convergence for inexact data is proved. Therefore the iterative implementation of the adaptive regularization can yield optimality.
Science in China Series a-Mathematics
"Iterative implementation of the adaptive regularization yields optimality" (2005). Faculty Bibliography 2000s. 5443.