A review on some parameter choice methods in Tikhonov regularization

Linear systems of equations with a large condition number are dificult to deal with. Because of their instability, standard methods such as Gaussian elimination method are not useful. These kind of equations need some regularization. Most of the regularization methods need a regularization parameter. Choosing optimal value for the regularization parameter is the heart of any regularization methods. In this paper we introduce and compare some parameter choice methods for Tikhonov regularization in 3 different situations well-estimate, under-estimate, and over-estimate considering of the noise level in right- hand side vector.