Efficient Calculations for k-diagonal Circulant Matrices and Cyclic Banded Matrices
CoRR(2024)
摘要
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.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要