Deriving Algorithms for Triangular Tridiagonalization a (Skew-)Symmetric Matrix

We apply the FLAME methodology to derive algorithms hand in hand with their proofs of correctness for the computation of the $ L T L^T $ decomposition (with and without pivoting) of a skew-symmetric matrix. The approach yields known as well as new algorithms, presented using the FLAME notation. A number of BLAS-like primitives are exposed at the core of blocked algorithms that can attain high performance. The insights can be easily extended to yield algorithms for computing the $ L T L^T $ decomposition of a symmetric matrix.