论文标题
Krylov子空间回收用于矩阵函数
Krylov Subspace Recycling For Matrix Functions
论文作者
论文摘要
我们通过子空间回收来得出一种增强的Krylov子空间方法，用于计算一组向量上的矩阵函数应用程序。矩阵是固定的，要么随着序列的进展而变化。我们假设连续的矩阵密切相关，但对向量之间的关系没有任何假设。我们提出该方法的三个版本，具有不同的实际实现。我们使用一系列具有功能和矩阵的数值实验来证明该方法的有效性。我们主要将注意力集中在晶格QCD的重叠形式主义中产生的符号函数。
We derive an augmented Krylov subspace method with subspace recycling for computing a sequence of matrix function applications on a set of vectors. The matrix is either fixed or changes as the sequence progresses. We assume consecutive matrices are closely related, but make no assumptions on the relationship between the vectors. We present three versions of the method with different practical implementations. We demonstrate the effectiveness of the method using a range of numerical experiments with a selection of functions and matrices. We primarily focus our attention on the sign function arising in the overlap formalism of lattice QCD.
