On the reduction of a Hamiltonian matrix to Hamiltonian Schur form. (English) Zbl 1115.65049
Summary: Recently D. Chu, X. Liu and V. Mehrmann [Numer. Math. 105, No. 3, 375–412 (2007; Zbl 1116.65043)] developed an \(O(n^3)\) structure preserving method for computing the Hamiltonian real Schur form of a Hamiltonian matrix. This paper outlines an alternative derivation of the method and an alternative explanation of why the method works. Our approach places emphasis on eigenvalue swapping and relies less on matrix manipulations.
MSC:
65F30 | Other matrix algorithms (MSC2010) |
65F15 | Numerical computation of eigenvalues and eigenvectors of matrices |
15A24 | Matrix equations and identities |