in this paper, we propose an algorithm for numerical solving an inverse non-linear diusion problem. in additional, the least-squares method is adopted tond the solution. to regularize the resultant ill-conditioned linear system ofequations, we apply the tikhonov regularization method to obtain the stablenumerical approximation to the solution. some numerical experiments con-rm the utility of...

We are concerned with polynomial ordinary differential systems that arise from modelling chemical reaction networks. For such systems, which may be of high dimension and depend on many parameters, it is frequently interest to obtain a reduction in certain parameter ranges. Singular perturbation theory, as initiated by Tikhonov Fenichel, provides path toward reductions. In the present paper we d...

Abstract This paper considers large-scale linear ill-posed inverse problems whose solutions can be represented as sums of smooth and piecewise constant components. To solve such we consider regularizers consisting two terms that must balanced. Namely, a Tikhonov term guarantees the smoothness solution component, while total-variation (TV) regularizer promotes blockiness non-smooth component. A ...

Ensemble Kalman inversion (EKI) is a derivative-free optimizer aimed at solving inverse problems, taking motivation from the celebrated ensemble filter. The purpose of this article to consider introduction adaptive Tikhonov strategies for EKI. This work builds upon EKI (TEKI) which was proposed fixed regularization constant. By adaptively learning parameter, procedure known improve recovery und...