多项式矩阵秩轮廓的秩敏感计算

Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation Pub Date : 2022-02-18 DOI:10.1145/3476446.3535495

G. Labahn, Vincent Neiger, Thi Xuan Vu, Wei Zhou

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引用次数: 1

摘要

考虑域K上的单变量多项式的矩阵F ε K [x]^mxn。我们研究了F的列秩轮廓的计算问题。为此，我们首先给出了一种算法，该算法改进了Zhou, Labahn和Storjohann的最小核基算法(Proceedings ISSAC 2012)。然后，我们提供了第二种算法，该算法计算F的列秩轮廓，其秩敏感复杂度为k中的O~ (rw-2n(m+d))次操作。这里，d是F的行度和，w是矩阵乘法的指数，O~(.)隐藏对数因子。

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Rank-Sensitive Computation of the Rank Profile of a Polynomial Matrix

Consider a matrix F ε K [x]^mxn of univariate polynomials over a field K. We study the problem of computing the column rank profile of F. To this end we first give an algorithm which improves the minimal kernel basis algorithm of Zhou, Labahn, and Storjohann (Proceedings ISSAC 2012). We then provide a second algorithm which computes the column rank profile of F with a rank-sensitive complexity of O~ (rw-2n(m+d)) operations in K. Here, D is the sum of row degrees of F, w is the exponent of matrix multiplication, and O~ (.) hides logarithmic factors.

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Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation

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