ELA STRUCTURE PRESERVING ALGORITHMS FOR PERPLECTIC EIGENPROBLEMS∗

Abstract. Structured real canonical forms for matrices in Rn×n that are symmetric or skew-symmetric about the anti-diagonal as well as the main diagonal are presented, and Jacobi algorithms for solving the complete eigenproblem for three of these four classes of matrices are developed. Based on the direct solution of 4 × 4 subproblems constructed via quaternions, the algorithms cal-culate structured orthogonal bases for the invariant subspaces of the associated matrix. In addition to preserving structure, these methods are inherently parallelizable, numerically stable, and show asymptotic quadratic convergence