Algorithm 682: Talbot's method of the Laplace inversion problems
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Algorithms for Parameter Selection in the Weeks Method for Inverting the Laplace Transform
SIAM Journal on Scientific Computing
Optimizing Talbot’s Contours for the Inversion of the Laplace Transform
SIAM Journal on Numerical Analysis
Application of Post's formula to optical pulse propagation in dispersive media
Computers & Mathematics with Applications
CUDA by Example: An Introduction to General-Purpose GPU Programming
CUDA by Example: An Introduction to General-Purpose GPU Programming
Classic Works of the Dempster-Shafer Theory of Belief Functions
Classic Works of the Dempster-Shafer Theory of Belief Functions
Hi-index | 0.09 |
In this paper, the Dempster-Shafer theory of evidential reasoning is applied to the problem of optimal contour parameters selection in Talbot's method for the numerical inversion of the Laplace transform. The fundamental concept is the discrimination between rules for the parameters that define the shape of the contour based on the features of the function to invert. To demonstrate the approach, it is applied to the computation of the matrix exponential via numerical inversion of the corresponding resolvent matrix. Training for the Dempster-Shafer approach is performed on random matrices. The algorithms presented have been implemented in MATLAB. The approximated exponentials from the algorithm are compared with those from the rational approximation for the matrix exponential returned by the MATLAB expm function.