Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Udgivet: |
2024
|
| Fag: | |
| Online adgang: | https://arxiv.org/abs/2411.19086 |
| Tags: |
Tilføj Tag
Ingen Tags, Vær først til at tagge denne postø!
|
Indholdsfortegnelse:
- We propose a quadrature-based formula for computing the exponential function of matrices with a non-oscillatory integral on an infinite interval and an oscillatory integral on a finite interval. In the literature, existing quadrature-based formulas are based on the inverse Laplace transform or the Fourier transform. We show these expressions are essentially equivalent in terms of complex integrals and choose the former as a starting point to reduce computational cost. By choosing a simple integral path, we derive an integral expression mentioned above. Then, we can easily apply the double-exponential formula and the Gauss-Legendre formula, which have rigorous error bounds. As numerical experiments show, the proposed formula outperforms the existing formulas when the imaginary parts of the eigenvalues of matrices have large absolute values.