A divide-and-conquer algorithm for a symmetric tri-block-diagonal matrix

We propose a stable and efficient divide-and-conquer algorithm for computing the eigendecomposition of a symmetric tri-block-diagonal matrix. The matrix can be derived from discretizing Laplace operator eigenvalue in some two-dimensional graphs. All numerical results show that our algorithm is competitive with other methods, such as e.g QR algorithm, Cuppen's divide-and-conquer algorithm. We also show how to improve our algorithm by Fast Multipole Method.