Generalised Sequential Matrix Diagonalisation for the SVD of Polynomial Matrices

To extend the singular value decomposition (SVD) to matrices of polynomials, an existing algorithm — a polynomial version of the Kogbetliantz SVD — iteratively targets the largest off-diagonal elements, and eliminates these through delay and Givens operations. In this paper, we perform a complete diagonalisation of the matrix component that contains this maximum element, thereby transfering more off-diagonal energy per iteration step. This approach is motivated by — and represents a generalisation of — the sequential matrix diagonalisation (SMD) method for parahermitian matrices. In simulations, we demonstrate the benefit of this generalised SMD over the Kogbetliantz approach, both in terms of diagonalisation and the order of the extracted factors.