一种用于反演扇形Laplace变换的谱阶方法

拉普拉斯变换数值反演中塔洛特算法的噪声处理特性

The Noise Handling Properties of the Talbot Algorithm for Numerically Inverting the Laplace Transform

本文研究了三种常用拉普拉斯变换反演算法的噪声处理能力，发现塔洛特算法在处理噪声数据时表现优异，优于傅里叶级数和斯特菲斯特算法。

从实轴反演拉普拉斯变换的自适应迭代方法

Inversion of the Laplace transform from the real axis using an adaptive iterative method

提出一种基于求积公式的自适应迭代方法，用于从实轴反演拉普拉斯变换，并证明近似解收敛到未知函数。

简约卷积求积法

Parsimonious convolution quadrature

本文提出简约卷积求积法，通过拉普拉斯域分段多项式插值将隐式欧拉和二阶后向差分格式下N步CQ近似的求值次数降至O(√N log N)或O(log² N)，适用于声学与电磁散射等半空间算子族，并给出理论分析与数值验证。

Computing first passage times for Markov-modulated fluid models using numerical PDE problem solvers

A popular method to compute first-passage probabilities in continuous-time Markov chains is by numerically inverting their Laplace transforms. Past decades, the scientific computing community has developed excellent numerical methods for solving problems governed by partial differential equations (PDEs), making the availability of a Laplace transform not necessary here for computational purposes. In this study we demonstrate that numerical PDE problem solvers are suitable for computing first passage times, and can be very efficient for this purpose. By doing extensive computational experiments…

基于拉普拉斯变换的量子特征值变换：通过哈密顿模拟的线性组合

Laplace transform based quantum eigenvalue transformation via linear combination of Hamiltonian simulation

提出一种基于拉普拉斯变换的量子特征值变换算法，扩展LCHS方法以处理矩阵逆的幂和指数，无需显式求逆矩阵，降低计算复杂度。

一种用于从质子结构函数获取胶子分布的逆拉普拉斯变换的新数值方法

A new numerical method for inverse Laplace transforms used to obtain gluon distributions from the proton structure function

针对逆拉普拉斯变换中函数衰减慢于1/s的情况，提出一种适用于任意正β和非整数负β的新数值算法，并通过数值测试和胶子分布演化验证其有效性。