Adaptive parameter choice for one-sided finite difference schemes and its application in diabetes technology
Let \(y\in C^r[b,\,B]\) \((r\geq 2)\). Assume that only noisy values \(y_{\delta}(t_j)\) with \(|y(t_j) - y_{\delta}(t_j)|\leq \delta\) on a grid \(b\leq t_1 < \ldots < t_{N-1}<t_N =B\) are given. Using one-sided finite difference formulas (with \(n+1\) values \(y_{\delta}(t_j)\)), the authors compute an approximate value of \(y'(B)\). The number \(n\) is used as regularization parameter of this ill-posed problem of numerical differentiation. The selection of an optimal parameter \(n\) is based on the balancing principle of \textit{S. Lu} and \textit{S. V. Pereverzev} [Math. Comput. 75, No. 256, 1853--1870 (2006; Zbl 1115.65021)]. For theoretical data as well as for simulated clinical data of diabetes therapy (of blood glucose prediction), numerical tests are shown.
scientific article; zbMATH DE number 6092441
scientific article