We investigate a novel adaptive choice rule of the Tikhonov regularization parameter in numerical differentiation which is a classic ill-posed problem. By assuming a general unknown Holder type error estimate derived ...We investigate a novel adaptive choice rule of the Tikhonov regularization parameter in numerical differentiation which is a classic ill-posed problem. By assuming a general unknown Holder type error estimate derived for numerical differentiation, we choose a regularization parameter in a geometric set providing a nearly optimal convergence rate with very limited a-priori information. Numerical simulation in image edge detection verifies reliability and efficiency of the new adaptive approach.展开更多
文摘We investigate a novel adaptive choice rule of the Tikhonov regularization parameter in numerical differentiation which is a classic ill-posed problem. By assuming a general unknown Holder type error estimate derived for numerical differentiation, we choose a regularization parameter in a geometric set providing a nearly optimal convergence rate with very limited a-priori information. Numerical simulation in image edge detection verifies reliability and efficiency of the new adaptive approach.
