A posteriori stopping rule for regularized fixed point iterations Original Research Article

Iteratively regularized fixed-point iteration scheme xn+1=xn-αn{F(xn)-fδ+εn(xn-x0)}xn+1=xn-αn{F(xn)-fδ+εn(xn-x0)} Turn MathJax on combined with the generalized discrepancy principle View the MathML source∥F(xN)-fδ∥2⩽τδ<∥F(xn)-fδ∥2,0⩽n1, Turn MathJax on for solving nonlinear operator equation F(x)=fF(x)=f in a Hilbert space is studied in the paper. It is shown that if FF is monotone and Lipschitz-continuous the sequence {N(δ)}{N(δ)} is admissible, i.e. equation(1) View the MathML sourcelimδ→0∥xN(δ)-x*∥=0, Turn MathJax on where x*x* is a solution to F(x)=fF(x)=f.