Before revision:  The results show that  the solution accuracy of the inner least squares problems can be relaxed considerably while it will not reduce the accuracy of regularized solutions, thus the overall efficiency of the algorithms can be improved substantially .
After revision:  The results show that for ill-posed problems with not too small noise levels, the solution accuracy of the inner least squares problems can be relaxed considerably while it will not reduce the accuracy of regularized solutions, thus the overall efficiency of the algorithms can be improved substantially .