کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4639789 | 1341251 | 2012 | 8 صفحه PDF | دانلود رایگان |
Over the last 2525 years, various fast algorithms for computing the determinant of a pentadiagonal Toeplitz matrices were developed. In this paper, we give a new kind of elementary algorithm requiring 56⋅⌊n−4k⌋+30k+O(logn) operations, where k≥4k≥4 is an integer that needs to be chosen freely at the beginning of the algorithm. For example, we can compute det(Tn)det(Tn) in n+O(logn)n+O(logn) and 82n+O(logn) operations if we choose kk as 5656 and ⌊2815(n−4)⌋, respectively. For various applications, it will be enough to test if the determinant of a pentadiagonal Toeplitz matrix is zero or not. As in another result of this paper, we used modular arithmetic to give a fast algorithm determining when determinants of such matrices are non-zero. This second algorithm works only for Toeplitz matrices with rational entries.
Journal: Journal of Computational and Applied Mathematics - Volume 236, Issue 9, March 2012, Pages 2298–2305