Discrepancy principle for DSM II

摘要

Let Ay =f, A is a linear operator in a Hilbert space H, y ⊥ N(A) := {u : Au = 0}, R(A) := {h:h = Au, u ∈ D(A)} is not closed, ||f_δ -f|| ≤ δ. Given f_δ, one wants to construct u_δ such that lim_(δ→0)||u_δ-y|| = 0. Two versions of discrepancy principles fo