matfree.bounds

matfree.bounds

Bounds on functions of matrices.

matfree.bounds.baigolub96_logdet_spd(bound_spectrum, /, nrows, trace, norm_frobenius_squared)

Bound the log-determinant of a symmatric, positive definite matrix.

This function implements Theorem 2 in the paper by Bai and Golub (1996).

bound_spectrum is either an upper or a lower bound on the spectrum of the matrix. If it is an upper bound, the function returns an upper bound of the log-determinant. If it is a lower bound, the function returns a lower bound of the log-determinant.

BibTex for Bai and Golub (1996)

@article{bai1996bounds,
    title={Bounds for the trace of the inverse and the
    determinant of symmetric positive definite matrices},
    author={Bai, Zhaojun and Golub, Gene H},
    journal={Annals of Numerical Mathematics},
    volume={4},
    pages={29--38},
    year={1996},
    publisher={Citeseer}
}