论文标题
理性的Krylov方法用于图形上的分数扩散问题
Rational Krylov methods for fractional diffusion problems on graphs
论文作者
论文摘要
在本文中，我们提出了一种计算有向网络分数扩散方程的解决方案的方法，该方法可以用图形laplacian $ l $作为产品$ f（l^t）\ boldsymbol {b} $表示，其中$ f $是涉及分数的幂和$ \ boldsymbol \ boldsymbol^iS a a n a $ f $。图laplacian是一个单数矩阵，导致$ f（l^t）\ boldsymbol {b} $的Krylov方法更慢地收敛。为了克服这一难度并实现更快的收敛性，我们使用适用于图形laplacian的降低版本的Rational Krylov方法，该方法以排名一偏移或在子空间上的投影获得。
In this paper we propose a method to compute the solution to the fractional diffusion equation on directed networks, which can be expressed in terms of the graph Laplacian $L$ as a product $f(L^T) \boldsymbol{b}$, where $f$ is a non-analytic function involving fractional powers and $\boldsymbol{b}$ is a given vector. The graph Laplacian is a singular matrix, causing Krylov methods for $f(L^T) \boldsymbol{b}$ to converge more slowly. In order to overcome this difficulty and achieve faster convergence, we use rational Krylov methods applied to a desingularized version of the graph Laplacian, obtained with either a rank-one shift or a projection on a subspace.
