Comparison of time complexity growth for different methods/algorithms for rectangular determinant calculations
Armend Salihu, Halil Snopçe, Artan Luma, Jaumin Ajdari · 2023
This article examines the asymptotic time complexity development for several approaches to compute the rectangular determinants. In this analysis are taken into consideration the Cullis/Radic method which has asymptotic time complexity of$O\left(C\binom {n}{m}\cdot m^{3}\right)$, Laplace method with the asymptotic time complexity calculated as$O(m!\cdot(n-m))$, Chios-like method that has asymptotic time complexity as$o(m^{2}\cdot n\cdot(n-m))$and Dodgson's condensation methods which have asymptotic time complexity of$O(2^{2m}\cdot(n-m)^{2})$. According to the calculations of time complexity growth for different order of matrices, the Chios-like method is the most useful method for computing rectangular matrices' determinant.