Abstract In the numerical methods for the Laplace transform inversion the errors quantification in computational processes is a crucial issue. In this paper, we propose two inversion methods based on smoothing splines combined with a procedure for the derivation of error bounds. In particular, we numerically study the impact of the fitting error amplification through the analysis of several sources of error and their propagation.

中文翻译：

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基于平滑样条的拉普拉斯变换反演计算误差界限

摘要 在拉普拉斯变换反演的数值方法中，计算过程中的误差量化是一个关键问题。在本文中，我们提出了两种基于平滑样条的反演方法，并结合了推导误差界的过程。特别是，我们通过对几种误差来源及其传播的分析，数值研究了拟合误差放大的影响。