We determine the probability, structure dependent, that the block Wiedemann algorithm correctly computes leading invariant factors. This leads to a tight lower bound for the probability, structure independent. We show, using block size slightly larger than r, that the leading r invariant factors are computed correctly with high probability over any field. Moreover, an algorithm is provided to compute the probability bound for a given matrix size and thus to select the block size needed to obtain the desired probability. The worst case probability bound is improved, post hoc, by incorporating the partial information about the invariant factors.

中文翻译：

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领先不变因子的分块 Wiedemann 概率分析

我们确定块 Wiedemann 算法正确计算主要不变因子的概率（结构相关）。这导致概率的下限严格，结构独立。我们表明，使用略大于r 的块大小，可以在任何领域以高概率正确计算前导r不变因子。此外，提供了一种算法来计算给定矩阵大小的概率界限，从而选择获得所需概率所需的块大小。通过结合关于不变因素的部分信息，事后改进了最坏情况概率界限。