论文标题
关于Gaver-Stehfest算法的收敛速率
On the rate of convergence of the Gaver-Stehfest algorithm
论文作者
论文摘要
Gaver-Stehfest算法广泛用于拉普拉斯变换的数值反转。在本文中，我们对Gaver-Stehfest算法的收敛速率进行了首次严格研究。我们证明，如果目标函数在一个点附近分析，并且如果目标函数为$（2K+3）$ - times times在某个点，则它们以速率$ o（n^{ - k}）$收敛，并且它们以速率$ o（n^{ - k}）$收敛。
The Gaver-Stehfest algorithm is widely used for numerical inversion of Laplace transform. In this paper we provide the first rigorous study of the rate of convergence of the Gaver-Stehfest algorithm. We prove that Gaver-Stehfest approximations converge exponentially fast if the target function is analytic in a neighbourhood of a point and they converge at a rate $o(n^{-k})$ if the target function is $(2k+3)$-times differentiable at a point.
