On the determinant evaluation of quasi penta-diagonal matrices and quasi penta-diagonal Toeplitz matrices

Recently, three computational algorithms for evaluating the determinant of quasi penta-diagonal matrices have been proposed by El-Mikkawy and Rahmo (Comput Math Appl 59:1386-1396, 2010), by Neossi Nguetchue and Abelman (Appl Math Comput 203:629-634, 2008), and by Jia et al. (Int J Comput Math 89:851-860, 2013), respectively. In the current paper, two novel algorithms with less computational costs are proposed for the determinant evaluation of general quasi penta-diagonal matrices and quasi penta-diagonal Toeplitz matrices. Furthermore, three numerical experiments are given to show the performance of our algorithms. All of the numerical computations were performed on a computer with aid of programs written in MATLAB.