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A fast algorithm for computing the determinants of banded circulant matrices

Xie-Bin Chen
Organization: College of Mathematics and Statistics, Minnan Normal University
Journal / Anthology

Applied Mathematics and Computation
Year: 2014
Volume: 229
Page range: 201-207

Let Cn be a k 1-diagonal complex circulant matrix of order n k 1, and let det Cn be the determinant of Cn. An algorithm for computing det Cn is presented with the cost of O klog2k  log2n k4   multiplication, and an asymptotic formula for det Cn is obtained. Moreover, a result on symmetric circulant matrices with integer entries is also given. Using Mathematica in a personal computer, we give some numerical examples, which illustrate that the algorithm is very efficient and the asymptotic formula is accurate enough when the order n of the circulant matrix is sufficiently large.

*Applied Mathematics