A Monte Carlo algorithm for efficient large matrix inversion
<|reference_start|>A Monte Carlo algorithm for efficient large matrix inversion: This paper introduces a new Monte Carlo algorithm to invert large matrices. It is based on simultaneous coupled draws from two random vectors whose covariance is the required inverse. It can be considered a generalization of a previously reported algorithm for hermitian matrices inversion based in only one draw. The use of two draws allows the inversion on non-hermitian matrices. Both the conditions for convergence and the rate of convergence are similar to the Gauss-Seidel algorithm. Results on two examples are presented, a real non-symmetric matrix related to quantitative genetics and a complex non-hermitian matrix relevant for physicists. Compared with other Monte Carlo algorithms it reveals a large reduction of the processing time showing eight times faster processing in the examples studied.<|reference_end|>
@article{garcia-cortes2004a,
    title={A Monte Carlo algorithm for efficient large matrix inversion},
    author={L. A. Garcia-Cortes and C. Cabrillo},
    journal={arXiv preprint arXiv:cs/0412107},
    year={2004},
    archivePrefix={arXiv},
    eprint={cs/0412107},
    primaryClass={cs.DS cs.NA hep-lat}
}