k 对角圆周矩阵和环带矩阵的高效计算

Chen Wang, Chao Wang
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引用次数: 0

摘要

计算$k$对角环形矩阵和环形带状矩阵的逆是一个比计算它们的行列式更具挑战性的问题。本文提出了两种快速算法,可以在复杂度为 $O(k^3 \log n+k^4)+kn$ 的范围内计算 $k$ 对角环带矩阵的复杂度,而对于 $k$ 对角环带矩阵,计算复杂度为 $O(k^3 n+k^5)+kn^2$ 。由于 $k$ 通常比 $n$ 小得多,这两种算法的成本可以近似为 $kn$ 和 $kn^2$。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Efficient Calculations for k-diagonal Circulant Matrices and Cyclic Banded Matrices
Calculating the inverse of $k$-diagonal circulant matrices and cyclic banded matrices is a more challenging problem than calculating their determinants. Algorithms that directly involve or specify linear or quadratic complexity for the inverses of these two types of matrices are rare. This paper presents two fast algorithms that can compute the complexity of a $k$-diagonal circulant matrix within complexity $O(k^3 \log n+k^4)+kn$, and for $k$-diagonal cyclic banded matrices it is $O(k^3 n+k^5)+kn^2$. Since $k$ is generally much smaller than $n$, the cost of these two algorithms can be approximated as $kn$ and $kn^2$.
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