A division-free algorithm for numerically evaluating the determinant of a specific quasi-tridiagonal matrix

Tridiagonal matrices and quasi-tridiagonal matrices frequently arise in the numerical simulations of biosensors and electrochemical systems, and have attracted attention in the past few years. In this paper, we present a division-free algorithm for evaluating the determinants of a class of quasi-tridiagonal matrices that can be viewed as perturbations of general tridiagonal matrices. The algorithm is based on a three-term recurrence relation for the determinants of general tridiagonal matrices. Compared with other related algorithms, the main advantage of the proposed algorithm is that it will never suffer from breakdown, even though it is not a symbolic algorithm. In addition, our proposed algorithm has a potential for parallel processing. The results of some numerical experiments are provided to demonstrate the validity and effectiveness of the proposed algorithm and its competitiveness with other related algorithms and MATLAB built-in function.