Deriving Algorithms for Triangular Tridiagonalization a Skew-Symmetric Matrix

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 $LT{L}^T$ 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.

28 pages. arXiv admin note: text overlap with arXiv:2411.09859