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In the current paper the authors linked two methods in order to evaluate general n-th order tridiagonal determinants. A breakdown free numerical algorithm is developed for computing the inverse of any nxn general nonsingular tridiagonal matrix without imposing any constrains. The algorithm is suited for implementation using any computer language such as FORTRAN, PYTHON, MATLAB, MAPLE, C, C++, MACSYMA, ALGOL, PASCAL and JAVA. Some illustrative examples are presented., Comment: 15 pages

The principal minors of a tridiagonal matrix satisfy two-term and three-term recurrences [1, 2]. Based on these facts, the current article presents a new efficient and reliable hybrid numerical algorithm for evaluating general n-th order tridiagonal determinants in linear time. The hybrid numerical algorithm avoid all symbolic computations. The algorithm is suited for implementation using computer languages such as FORTRAN, PASCAL, ALGOL, MAPLE, MACSYMA and MATHEMATICA. Some illustrative examples are given. Test results indicate the superiority of the hybrid numerical algorithm., Comment: 12 pages, 2 figures