@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 = {<p style="text-align: justify;">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.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1503-m2014-0134},
url = {http://global-sci.org/intro/article_detail/jcm/9851.html}
}