@Article{CSIAM-AM-4-225,
author = {Tong , ShanshanWang , WeiFu , Zhenwu and Han , Bo},
title = {Iterative Runge-Kutta-Type Methods with Convex Penalty for Inverse Problems in Hilbert Spaces},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2023},
volume = {4},
number = {2},
pages = {225--255},
abstract = {<p style="text-align: justify;">An s-stage Runge-Kutta-type iterative method with the convex penalty for
solving nonlinear ill-posed problems is proposed and analyzed in this paper. The
approach is developed by using a family of Runge-Kutta-type methods to solve the
asymptotical regularization method, which can be seen as an ODE with the initial
value. The convergence and regularity of the proposed method are obtained under
certain conditions. The reconstruction results of the proposed method for some special cases are studied through numerical experiments on both parameter identification
in inverse potential problem and diffuse optical tomography. The numerical results
indicate that the developed methods yield stable approximations to true solutions, especially the implicit schemes have obvious advantages on allowing a wider range of
step length, reducing the iterative numbers, and saving computation time.</p>},
issn = {2708-0579},
doi = {https://doi.org/10.4208/csiam-am.SO-2022-0012},
url = {http://global-sci.org/intro/article_detail/csiam-am/21413.html}
}