论文标题
通过随机化加速用于计算F（a）b的Krylov子空间方法
Speeding up Krylov subspace methods for computing f(A)b via randomization
论文作者
论文摘要
这项工作与矩阵函数f（a）的作用（例如矩阵指数或矩阵平方根）在向量b上的计算有关。对于一般矩阵A，可以通过计算A对合适的Krylov子空间的压缩来完成。这种压缩通常是通过使用Arnoldi方法来形成Krylov子空间的正顺序基础来计算的。在这项工作中，我们建议以更快的方式计算（非正常）碱基，并使用快速的随机算法来解决最小二乘问题，以计算A在Krylov子空间上的压缩。我们提供了一些数值示例，这些示例表明我们的算法可以比标准Arnoldi方法更快，同时实现了可比的精度。
This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov subspace. Such compression is usually computed by forming an orthonormal basis of the Krylov subspace using the Arnoldi method. In this work, we propose to compute (non-orthonormal) bases in a faster way and to use a fast randomized algorithm for least-squares problems to compute the compression of A onto the Krylov subspace. We present some numerical examples which show that our algorithms can be faster than the standard Arnoldi method while achieving comparable accuracy.
