A finite splitting algorithm for a complex \(J\)-symmetric pencil (Q1802591)

The generalized eigenvalue problem \(Nx = \lambda Lx\) is called \(J\)- symmetric if \(NJL^ T = LJN^ T\), where \(J = ({0\atop -I_ n}{I_ n\atop 0})\), \(N,L \in \mathbb{C}^{2n\times 2n}\). The present paper gives a finite symplectic algorithm for reducing the problem to the same one of half dimension. The algorithm is explained in terms of changes to the analogous real problem [cf. the author, ibid. 30, No. 12, 1765-1774 (1990; Zbl 0717.65020)]. Also, a relation is established between the spectra of real Hamiltonian and \(J\)-symmetric pencils.