论文标题
QZ算法的新通缩标准
A new deflation criterion for the QZ algorithm
论文作者
论文摘要
QZ算法计算基质铅笔的Schur形式。它是一种迭代算法，在某个时候，它必须决定特征值已经融合并继续前进。选择一个使该决定的标准是不平凡的。如果太严格，算法可能会浪费在已经融合的特征值上的迭代。如果不够严格，则计算的特征值可能不准确。此外，评估标准在计算上不应昂贵。本文根据特征值之间的大小和差距介绍了一个新标准。这类似于QR算法的Ahues和Tissuer的工作。理论论点和数值实验表明，就准确性而言，它的表现优于最流行的标准。此外，本文评估了一些无限特征值的常用标准。
The QZ algorithm computes the Schur form of a matrix pencil. It is an iterative algorithm and at some point, it must decide that an eigenvalue has converged and move on with another one. Choosing a criterion that makes this decision is nontrivial. If it is too strict, the algorithm might waste iterations on already converged eigenvalues. If it is not strict enough, the computed eigenvalues might be inaccurate. Additionally, the criterion should not be computationally expensive to evaluate. This paper introduces a new criterion based on the size of and the gap between the eigenvalues. This is similar to the work of Ahues and Tissuer for the QR algorithm. Theoretical arguments and numerical experiments suggest that it outperforms the most popular criteria in terms of accuracy. Additionally, this paper evaluates some commonly used criteria for infinite eigenvalues.
