论文标题
Krylov子空间重新启动矩阵拉普拉斯变换
Krylov subspace restarting for matrix Laplace transforms
论文作者
论文摘要
近似$ f（a）b $的一种常见方法 - 矩阵函数在向量上的作用 - 是使用arnoldi近似。由于需要在每次迭代中生成并存储一个新的向量，因此通常被迫依靠重新启动算法，该算法要么不高，要么不稳定，要么仅适用于限制的功能类别。如果函数$ f $作为拉普拉斯变换，我们提出了Arnoldi误差的新表示形式。基于此表示，我们构建了一种高效稳定的重新启动算法。为此，我们扩展了较早的stieltjes函数类别的工作，这些功能是特殊的拉普拉斯变换。我们报告了几个数值实验，包括与stieltjes函数重新启动方法的比较。
A common way to approximate $F(A)b$ -- the action of a matrix function on a vector -- is to use the Arnoldi approximation. Since a new vector needs to be generated and stored in every iteration, one is often forced to rely on restart algorithms which are either not efficient, not stable or only applicable to restricted classes of functions. We present a new representation of the error of the Arnoldi iterates if the function $F$ is given as a Laplace transform. Based on this representation we build an efficient and stable restart algorithm. In doing so we extend earlier work for the class of Stieltjes functions which are special Laplace transforms. We report several numerical experiments including comparisons with the restart method for Stieltjes functions.
