Mackey, D. Steven; Mackey, Niloufer; Dunlavy, Daniel M. Structure preserving algorithms for perplectic eigenproblems. (English) Zbl 1065.65053 Electron. J. Linear Algebra 13, 10-39 (2005). This paper deals with structured real canonical forms for matrices in \(\mathbb R^{n\times n}\) that are symmetric about the anti-diagonal as well as the main diagonal. Jacobi algorithms are presented for three of the above four mentioned cases. In addition to preserving structures, these methods are inherently parallelizable, numerically stable, and show asymptotic quadratic convergence. Reviewer: Răzvan Răducanu (Iaşi) Cited in 16 Documents MSC: 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 15A21 Canonical forms, reductions, classification 15B57 Hermitian, skew-Hermitian, and related matrices 65F30 Other matrix algorithms (MSC2010) Keywords:canonical form; eigenvalues; eigenvectors; Jacobi method; double structure preserving; symmetric; persymmetry; skew-symmetric; perskew-symmetric; centrosymmetric; perplectic; quaternion; tensor product; Lie algebra; Jordan algebra; bilinear form; parallel computation; quadratic convergence PDFBibTeX XMLCite \textit{D. S. Mackey} et al., Electron. J. Linear Algebra 13, 10--39 (2005; Zbl 1065.65053) Full Text: DOI EuDML EMIS