Efficient scaling and squaring method for the matrix exponential
<|reference_start|>Efficient scaling and squaring method for the matrix exponential: This work presents a new algorithm to compute the matrix exponential within a given tolerance. Combined with the scaling and squaring procedure, the algorithm incorporates Taylor, partitioned and classical Pad\'e methods shown to be superior in performance to the approximants used in state-of-the-art software. The algorithm computes matrix--matrix products and also matrix inverses, but it can be implemented to avoid the computation of inverses, making it convenient for some problems. If the matrix A belongs to a Lie algebra, then exp(A) belongs to its associated Lie group, being a property which is preserved by diagonal Pad\'e approximants, and the algorithm has another option to use only these. Numerical experiments show the superior performance with respect to state-of-the-art implementations.<|reference_end|>
@article{blanes2024efficient,
    title={Efficient scaling and squaring method for the matrix exponential},
    author={Sergio Blanes, Nikita Kopylov, Muaz Seydaou{g}lu},
    journal={arXiv preprint arXiv:2404.12789},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.12789},
    primaryClass={math.NA cs.NA}
}