论文标题
Krylov-Aware Antakatic痕量估计
Krylov-aware stochastic trace estimation
论文作者
论文摘要
我们介绍了一种算法，用于估算使用具有对称矩阵$ \ Mathbf {a} $的隐式产品的矩阵函数$ f（\ mathbf {a}）$的跟踪。矩阵函数隐式跟踪估计的现有方法倾向于以$ f（\ mathbf {a} $作为黑框处理矩阵 - 矢量产物，以通过Krylov子空间方法计算。像其他最近的隐性痕量估计算法一样，我们的方法基于通缩和随机痕量估计的组合。但是，我们仔细研究了如何将$ f（\ mathbf {a}）$集成到这些方法中的产品如何使以前研究的方法中不存在几种效率。特别是，我们描述了一种Krylov子空间方法，用于通过计算有效投影在Krylov子空间上计算矩阵函数的低级别近似值。
We introduce an algorithm for estimating the trace of a matrix function $f(\mathbf{A})$ using implicit products with a symmetric matrix $\mathbf{A}$. Existing methods for implicit trace estimation of a matrix function tend to treat matrix-vector products with $f(\mathbf{A})$ as a black-box to be computed by a Krylov subspace method. Like other recent algorithms for implicit trace estimation, our approach is based on a combination of deflation and stochastic trace estimation. However, we take a closer look at how products with $f(\mathbf{A})$ are integrated into these approaches which enables several efficiencies not present in previously studied methods. In particular, we describe a Krylov subspace method for computing a low-rank approximation of a matrix function by a computationally efficient projection onto Krylov subspace.
