The problem of computing a kth root of a matrix product W = Pi (k)(i=1) A(i) is considered. The explicit computation of W may produce a highly inaccurate result due to rounding errors, such that the computed root (W) over cap (1/k) is far from the actual root W-1/k. An algorithm for computing the square root of W is presented which avoids the explicit computation of W by employing the periodic Schur decomposition and therefore yields better accuracy in the computed root Wa. In principle, the techniques are applicable to K > 2 as well but lead to solving 2 x 2 polynomial matrix: equations which are difficult to treat. The case k = 3 is also addressed briefly. [References: 4]
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机译：考虑了计算矩阵乘积W的第k个根的问题W ＝ Pi（k）（i ＝ 1）A（i）。由于舍入误差，W的显式计算可能会产生非常不准确的结果，从而使上限（1 / k）上的计算根（W）偏离实际根W-1 / k。提出了一种计算W的平方根的算法，该算法避免了通过采用周期性Schur分解进行W的显式计算，因此在计算出的Wa上具有更好的精度。原则上，这些技术也适用于K> 2，但会导致求解2 x 2多项式矩阵：难以处理的方程。 k = 3的情况也作了简要介绍。 [参考：4]
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