Aasen’s Symmetric Indefinite Linear Solvers in LAPACK

Recently, we released two LAPACK subroutines that implement Aasen’s algorithms for solving a symmetric indefinite linear system of equations. The first implementation is based on a partitioned right-looking variant of Aasen’s algorithm (the column-wise left-looking panel factorization, followed by the right-looking trailing submatrix update using the panel). The second implements the two-stage left-looking variant of the algorithm (the block-wise leftlooking algorithm that reduces the matrix to the symmetric band form, followed by the band LU factorization). In this report, we discuss our implementations and present our experimental results to compare the stability and performance of these two new solvers with those of the other two symmetric indefinite solvers in LAPACK (i.e., the Bunch-Kaufman and rook pivoting algorithms).