Simplified Landweber iteration with stopping rule for a class of ill-posed problems

The simplified Landweber iteration with stopping rule for a positive semi-definite,compact and self-adjoint operator equation is proposed.By special system of compact and self-adjoint operator-eigen-system,our simplified iteration strategy is presented and optimal convergence rate obtained.Finally,a numerical example is included to show the high accuracy of the method,which has great computational advantages over the traditional one.