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.
翻译：{{{{{{{{{{{{{}}}计算出基质铅笔的Schur形式。{{}}}它是一种迭代算法,在某点上,它必须决定一个二次数值已经趋同,并与另一次数值相接。选择一个标准来作出这个决定是非三边的。如果它太严格,则算法可能会在已经趋同的二次数值上浪费迭代。如果它不够严格,计算出的二次数值可能不准确。此外,计算出的二次数值可能不准确。该标准不应计算得昂贵。此标准不应计算得过高。此文件根据二次数值的大小和差距推出一个新的标准。这与Ahues和QR算法的质源器相似。}理论论和数字实验表明,它比最常用的标准准确性强。此外,本文评价了某些常用的无限的乙质值标准。
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