Regularization using QR factorization and the estimation of the optimal parameter

In this paper we propose a direct regularization method using QR factorization for solving linear discrete ill-posed problems. The decomposition of the coefficient matrix requires less computational cost than the singular value decomposition which is usually use for Tikhonov regularization. This method requires a parameter which is similar to the regularization parameter of Tikhonov's method. In order to estimate the optimal parameter, we apply three well-known parameter choice methods for Tikhonov regularization.