论文标题
平行的稳健计算基质铅笔的广义特征向量
Parallel Robust Computation of Generalized Eigenvectors of Matrix Pencils
论文作者
论文摘要
在本文中，我们考虑了以真实Schur形式计算基质铅笔的广义特征向量的问题。在确切的算术中，可以使用替换解决此问题。实际上，替代容易受到浮点溢出的影响。 Lapack中强大的求解器XTGEVC通过动态缩放特征向量来防止溢出。这些子例程是顺序标量代码，它一一计算特征向量。在本文中，我们讨论了如何得出可靠的阻塞算法。新的Starneig库包含一个强大的任务并行求解器Zazamoukh，它在Starpu的顶部运行。我们的数值实验表明，与DTGEVC相比，Zazamoukh实现了超级线性的速度。
In this paper we consider the problem of computing generalized eigenvectors of a matrix pencil in real Schur form. In exact arithmetic, this problem can be solved using substitution. In practice, substitution is vulnerable to floating-point overflow. The robust solvers xTGEVC in LAPACK prevent overflow by dynamically scaling the eigenvectors. These subroutines are sequential scalar codes which compute the eigenvectors one by one. In this paper we discuss how to derive robust blocked algorithms. The new StarNEig library contains a robust task-parallel solver Zazamoukh which runs on top of StarPU. Our numerical experiments show that Zazamoukh achieves a super-linear speedup compared with DTGEVC for sufficiently large matrices.
