A Kind of a Posteriori Parameter Choices for the Iterated Tikhonov Regularization Method

Abstract

Let X and Y be real Hilbert spaces and A: X→Y be a bounded linear operator with nonclosed range R(A). If y∈ D(A~+)=R(A)+R(A)~⊥, there exists a unique Moore-Penrose generalized solution to the equation Ax=y. In practice, however, the given equation is usually of an approximate form Ax=yδ, (1)