On the inverse and determinant of general bordered tridiagonal matrices

In the current paper, we present a symbolic algorithm, that never suffers from breakdown, for computing the inverse of general bordered tridiagonal matrices. Meanwhile, an explicit formula of evaluating the determinant of a bordered tridiagonal matrix is also derived. The implementation of the proposed algorithm using Computer Algebra Systems (CASs) is straightforward. Some numerical examples are given in order to demonstrate the performance and validity of the presented results.