We show how rational function approximations to the logarithm, such as log z ≈ (z² - 1)/(z² + 6z + 1), can be turned into fast algorithms for approximating the determinant of a very large matrix. We empirically demonstrate that when combined with a good preconditioner, the third order rational function approximation offers a very good trade-off between speed and accuracy when measured on matrices coming from Mat\'ern-$5/2$ and radial basis function Gaussian process kernels. In particular, it is significantly more accurate on those matrices than the state-of-the-art stochastic Lanczos quadrature method for approximating determinants while running at about the same speed.
No takes yet. Share an insight, caveat, or question.
Colthurst et al. (2024) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: