论文标题
比较遗传学矩阵stieltjes函数的有限内存Krylov方法
A comparison of limited-memory Krylov methods for Stieltjes functions of Hermitian matrices
论文作者
论文摘要
鉴于有限的内存和目标精度，我们提出并比较了几种多项式Krylov方法，即F（a）B的近似值，这是vector上大型Hermitian矩阵的stieltjes矩阵函数的作用。使用新的错误界限和估计以及现有结果，我们得出了对方法的实际性能的预测，并将其进行相应的排名。作为副产品，我们在矩阵函数的不精确krylov迭代中得出了新的结果，以便对有理学的Krylov方法与多项式内溶液进行公平比较。
Given a limited amount of memory and a target accuracy, we propose and compare several polynomial Krylov methods for the approximation of f(A)b, the action of a Stieltjes matrix function of a large Hermitian matrix on a vector. Using new error bounds and estimates, as well as existing results, we derive predictions of the practical performance of the methods, and rank them accordingly. As by-products, we derive new results on inexact Krylov iterations for matrix functions in order to allow for a fair comparison of rational Krylov methods with polynomial inner solves.
