FLAME-derived LTLT factorization algorithms for skew-symmetric matrices, with fused BLAS-like operations, greatly outperform PFAPACK and Pfaffine
This work systematically derives a family of algorithms for the LTLT (L unit lower triangular, T skew-symmetric tridiagonal) triangular tridiagonalization of a skew-symmetric matrix X using the FLAME methodology, presents unpivoted and pivoted blocked right-looking, left-looking, and fused variants, identifies new level-2 and level-3 BLAS-like operations, and implements them with BLIS 2.0 packing mechanisms and OpenMP parallelism; experiments show the best implementations greatly exceed the performance of the only known prior software, PFAPACK and Pfaffine, while matching or exceeding related symmetric factorization software.