几类循环矩阵的对数矩阵及其计算

The computation of the logarithms of several classes of circulant matrices

首先研究了k-循环矩阵、斜k-循环矩阵以及Hermitian k-循环矩阵的对数矩阵的结构,之后对这些对数矩阵进行了分类,并设计了计算这几种循环矩阵对数矩阵的算法,这些算法与基于Schur分解的反scaling and squaring算法相比,在计算效率上有较大提高.

The structures of the logarithms of k-circulant matrices, skew k-circulant matrices and Hermitian k-circu- lant matrices are investigated. Then the classifications of their logarithms are given. In the end, several algorithms for computing the logarithms are developed. It is showed that our algorithms are more efficient than the standard in- verse scaling and squaring method which is based on the Schur decomposition.