A numerical solver for general bordered tridiagonal matrix equations

To overcome several limitations of symbolic algorithms introduced recently for matrices of large order, a fast numerical solver is proposed for the matrix linear equation AX=B, where the n×n coefficient matrix A is a general nonsingular bordered tridiagonal matrix. Its sparse structure is preserved through partial Givens reduction. In particular, the matrix inverse of A can be computed. For a wide range of bordered tridiagonal linear systems Ax=b, the solution is computed in linear time using back substitution and Sherman-Morrison's formula. Numerical comparisons illustrate the results.