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.

翻译：本文运用FLAME方法论，同步推导了（斜）对称矩阵$ L T L^T $分解（含/不含主元选取）算法及其正确性证明。该方法既生成已知算法也生成新算法，并通过FLAME符号体系予以呈现。在可实现高性能的分块算法核心处，揭示了若干类BLAS基本运算单元。这些见解可轻松推广至对称矩阵$ L T L^T $分解算法的推导。