@Article{JCM-33-415, author = {Mao , Heng}, title = {Adaptive Choice of the Regularization Parameter in Numerical Differentiation}, journal = {Journal of Computational Mathematics}, year = {2015}, volume = {33}, number = {4}, pages = {415--427}, abstract = {

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 Hölder 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1503-m2014-0134}, url = {http://global-sci.org/intro/article_detail/jcm/9851.html} }