Deriving Algorithms for Triangular Tridiagonalization a Skew-Symmetric Matrix (2311.10700v2)

Abstract: This paper provides technical details regarding the application of 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, enabling comparing and contrasting. A number of BLAS-like primitives are exposed at the core of the resulting unblocked and blocked algorithms.