A Fast Compensated Algorithm for Computing Givens Rotations
<|reference_start|>A Fast Compensated Algorithm for Computing Givens Rotations: We develop a very simple compensated scheme for computing very accurate Givens rotations. The approach is significantly more straightforward than the one in \cite{borges2021fast}, and the derivation leads to a very satisfying algorithm whereby a naively computed Givens rotation can be used to construct a correction to itself. It is also seen that this scheme continues to provide high accuracy even when built on a hypoteneuse calculation that is of lesser accuracy.<|reference_end|>
@article{borges2024a,
    title={A Fast Compensated Algorithm for Computing Givens Rotations},
    author={Carlos F. Borges},
    journal={arXiv preprint arXiv:2406.02750},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.02750},
    primaryClass={math.NA cs.NA}
}