矩阵笔广义特征向量的并行鲁棒计算
Parallel Robust Computation of Generalized Eigenvectors of Matrix Pencils
摘要：
本文考虑实Schur型矩阵束的广义特征向量的计算问题。在精确算术中，这个问题可以通过代入来解决。在实践中，替换很容易发生浮点溢出。LAPACK中的鲁棒求解器xTGEVC通过动态缩放特征向量来防止溢出。这些子程序是顺序标量代码，逐个计算特征向量。在本文中，我们讨论如何获得强大的分块算法。新的StarNEig库包含一个强大的任务并行求解器Zazamoukh，它运行在StarPU之上。我们的数值实验表明，Zazamoukh实现了超线性加速比DTGEVC足够大的矩阵。
英文摘要：
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.
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