Before revision:  That is to say , the new method uses the L-BFGS method as the preconditioned technique to improve its computational efficiency in the well-posed phase . Otherwise, it uses the inverse of the regularization two-sided projected Hessian matrix as the pre-conditioner to improve its robustness.
After revision:  That is to say , the new method uses the L-BFGS method as the preconditioned technique to improve its computational efficiency in the well-posed phase , and it uses the inverse of the regularization two-sided projected Hessian matrix as the pre-conditioner to improve its robustness.