论文标题
过度确定和不确定的通用中心单纯形梯度的误差范围
Error bounds for overdetermined and underdetermined generalized centred simplex gradients
论文作者
论文摘要
使用Moore-Penrose Pseudoinverse，这项工作概括了称为中心单纯梯度的梯度近似技术，以允许包含任意数量的样品集。这种近似技术称为\ emph {广义中心的单纯形梯度}。我们开发误差界限，并在全级条件下表明误差界的顺序$ o（δ^2）$，其中$δ$是所使用的点样品集的半径。我们为通用中心的单纯形梯度建立了微积分规则，引入了基于微积分的概括中心的单纯形梯度，并确认这种新方法的错误界限也是$ O（δ^2）$的顺序。我们提供了几个示例，以说明这些新方法的结果和一些好处。
Using the Moore--Penrose pseudoinverse, this work generalizes the gradient approximation technique called centred simplex gradient to allow sample sets containing any number of points. This approximation technique is called the \emph{generalized centred simplex gradient}. We develop error bounds and, under a full-rank condition, show that the error bounds have order $O(Δ^2)$, where $Δ$ is the radius of the sample set of points used. We establish calculus rules for generalized centred simplex gradients, introduce a calculus-based generalized centred simplex gradient and confirm that error bounds for this new approach are also order $O(Δ^2)$. We provide several examples to illustrate the results and some benefits of these new methods.
