We consider the problem of estimating log-determinants of large, sparse, positive definite matrices. A key focus of our algorithm is to reduce computational cost, and it is based on sparse approximate inverses. The algorithm can be implemented to be adaptive, and it uses graph spline approximation to improve accuracy. We illustrate our approach on classes of large sparse matrices.

翻译：我们考虑大型稀疏正定矩阵的对数行列式估计问题。我们算法的核心目标是降低计算成本，其基础是稀疏近似逆矩阵。该算法可实现自适应，并利用图样条逼近来提高精度。我们通过多类大型稀疏矩阵对方法进行了验证。