Adaptive matrix exponential for given tolerance

[nakopylov]

What kind of problems is it mostly used for? Please describe.

Any general problem where one specifies the tolerance for the matrix exponential. For example, low-order exponential integrators when calculating the exp up to the round-off error is not really necessary.

Describe the algorithm you’d like

Given a tolerance, the algoritm chooses the cheapest method from superdiagonal Padé approximants decomposed into simpler fractions, which reduces the cost compared to the "default" diagonal Padés.

Other implementations to know about

Code used in the article:
Julia: https://zenodo.org/records/14264631
Matlab: https://zenodo.org/records/11082084

References

Paper: S. Blanes, N. Kopylov, M. Seydaoğlu. "Efficient Scaling and Squaring Method for the Matrix Exponential". https://doi.org/10.1137/24M1657250
Arxiv: https://arxiv.org/abs/2404.12789