Comparison of Tikhonov regularization and Adaptive regularization for ill-posed problems

Inverse problems are important interdisciplinary subject, which receive more and more attention in recent years in the areas of mathematics, computer science, information science and other applied natural sciences. There is close relationship between inverse problems and ill-posedness. Regularization is an important strategy when computing the ill-posed problems to maintain the stability of the computation. This paper compares a new regularization method, which is called Adaptive regularization, with the traditional Tikhonov regularization method. The conclusion that Adaptive regularization method is a stronger regularization method than the traditional Tikhonov regularization method can be made by computing some numerical examples.