Estimation of the Derivatives of a Digital Function with a Convergent Bounded Error
Estimation of the Derivatives of a Digital Function with a Convergent Bounded Error
复制标题
具有收敛有界误差的数字函数导数的估计
DOI：
10.1007/978-3-642-19867-0_24
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Y. Gérard
中科院分区：
文献类型：
--
作者：
Laurent Provot;Y. Gérard
本文提出了一种用线性规划或其它几何算法估计数字函数导数的新方法。已知具有分辨率h的真实的连续函数f的数字化，该方法提供k阶导数f（k）（x）的具有最大误差的近似，其中常数取决于x的邻域中的（k+ 1）阶导数f的绝对值的上界。这种收敛速度应该与已经提供这种一致收敛结果的另外两种方法，即Lachaudet的方法进行比较。al（仅适用于一阶导数）和来自Malgouyreset al。
We provide a new method to estimate the derivatives of a digital function by linear programming or other geometrical algorithms. Knowing the digitization of a real continuous functionfwith a resolutionh, this approach provides an approximation of thekthderivativef(k)(x) with a maximal error inwhere the constant depends on an upper bound of the absolute value of the (k+ 1)thderivative offin a neighborhood ofx. This convergence rateshould be compared to the two other methods already providing such uniform convergence results, namelyfrom Lachaudet. al(only for the first order derivative) andfrom Malgouyreset al..