A novel algorithm for calculating the singular value decomposition of a polynomial matrix

A novel algorithm for calculating the singular value decomposition (SVD) of a polynomial matrix is proposed. The algorithm operates by iteratively calculating the QR decomposition (QRD) of the matrix to transform it to a diagonal polynomial matrix. Alternatively, this decomposition can be calculated using the polynomial matrix eigenvalue decomposition (EVD) routine known as the second-order sequential best rotation (SBR2) algorithm. However, this method does not operate directly on the polynomial matrix. Instead, it formulates the left and right singular vectors in turn, by calculating the EVD of two para-Hermitian matrices formed from the polynomial matrix. The advantage of the algorithm proposed in this paper, is that it does operate directly upon the polynomial matrix and can therefore allow significantly more control over the level of decomposition performed. The two approaches are compared by means of computer simulations which demonstrates that the method based on the polynomial matrix QRD algorithm is numerically superior.