I am looking for a good numerical method to solve a linear system (of small/moderate size) with a matrix of the form
$$
\begin{bmatrix}
a\_1 & b\_1\\
& a\_2 & \ddots \\
& & \ddots & b\_{n-1}\\
b\_n & & & a\_n
\end{bmatrix}.
$$
What would you suggest?

Entries not displayed are zero. The $a\_i$ and $b\_i$ entries can be arbitrary, so I would not trust the stability of unpivoted Gaussian elimination.

Related question: [solving system of linear equations with cyclic tridiagonal matrix](https://scicomp.stackexchange.com/questions/10137/solving-system-of-linear-equations-with-cyclic-tridiagonal-matrix).