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A fast algorithm for computing the determinants of banded circulant matrices
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| Organization: | College of Mathematics and Statistics, Minnan Normal University |
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| Applied Mathematics and Computation |
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Let Cn be a ðk þ 1Þ-diagonal complex circulant matrix of order nð k þ 1Þ, and let det Cn be the determinant of Cn. An algorithm for computing det Cn is presented with the cost of O klog2k log2n þ 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.
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