Efficient algorithm for the oscillatory matrix functions
<|reference_start|>Efficient algorithm for the oscillatory matrix functions: This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and restoring technique based on a quadruple angle formula in conjunction with a truncated Taylor series. The choice of the scaling parameter and the degree of the Taylor polynomial relies on a forward error analysis. Numerical experiments show that the new algorithm behaves in a stable fashion and performs well in both accuracy and efficiency.<|reference_end|>
@article{li2024efficient,
    title={Efficient algorithm for the oscillatory matrix functions},
    author={Dongping Li, Xue Wang, Xiuying Zhang},
    journal={arXiv preprint arXiv:2406.06008},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.06008},
    primaryClass={math.NA cs.NA}
}