A Numerical Method for Computing an SVD-like Decomposition

Abstract

We present a numerical method for computing the SVD-like decomposition B = QDS-1 , where Q is orthogonal, S is symplectic, and D is a permuted diagonal matrix. The method can be applied directly to compute the canonical form of the Hamiltonian matrices of the form JBTB , where $J=[{0 \atop -I}{I \atop 0}]$. It can also be applied to solve the related application problems such as the gyroscopic systems and linear Hamiltonian systems. Error analysis and numerical examples show that the eigenvalues of JBTB computed by this method are more accurate than those computed by the methods working on the explicit product JBTB or BJBT .