In this paper, we present new a posteriori and a priori error bounds for theKrylov subspace methods for computing $e^{-\tau A}v$ for a given $\tau>0$ and$v \in C^n$, where $A$ is a large sparse non-Hermitian matrix. The {\em apriori} error bounds relate the convergence to$\lambda_{\min}\left(\frac{A+A^*}{2}\right)$,$\lambda_{\max}\left(\frac{A+A^*}{2}\right)$ (the smallest and the largesteigenvalue of the Hermitian part of $A$) and$|\lambda_{\max}\left(\frac{A-A^*}{2}\right)|$ (the largest eigenvalue inabsolute value of the skew-Hermitian part of $A$), which define a rectangularregion enclosing the field of values of $A$. In particular, our bounds explainan observed superlinear convergence behavior where the error may first stagnatefor certain iterations before it starts to converge. The special case that $A$is skew-Hermitian is also considered. Numerical examples are given todemonstrate the theoretical bounds.
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机译：在本文中，我们针对给定$ \ tau> 0 $和$ v \ in C ^ n $的情况下，用于计算$ e ^ {-\ tau A} v $的Krylov子空间方法，提出了新的后验和先验误差界，其中$ A $是一个大型的稀疏非Hermitian矩阵。 {\ em apriori}错误界限将收敛与$ \ lambda _ {\ min} \ left（\ frac {A + A ^ *} {2} \ right）$，$ \ lambda _ {\ max} \ left（\ frac {A + A ^ *} {2} \ right）$（$ A $的埃尔米特部分的最小和最大特征值）和$ | \ lambda _ {\ max} \ left（\ frac {AA ^ *} { 2} \ right）| $（$ A $的倾斜-Hermitian部分的最大特征值非绝对值），它定义了一个矩形区域，该区域包围了$ A $的值字段。特别是，我们的边界解释了观察到的超线性收敛行为，其中误差在开始收敛之前可能会先停滞某些迭代。还考虑了$ A $是偏斜Hermitian的特殊情况。数值例子说明了理论范围。
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