Cholesky-like Factorizations of Skew-Symmetric Matrices
Peter Benner, Ralph E. Byers, Heike Faßbender, Volker Mehrmann, David S. Watkins · 2000
Every real skew-symmetric matrix B admits Cholesky-like factorizations B = R T JR where J = h 0 \\GammaI I 0 i . This paper presents a backward-stable O(n³) process for computing such a decomposition, in which R is a permuted triangular matrix. Decompositions of this type are a key ingredient of algorithms for solving eigenvalue problems with Hamiltonian structure.