Generalized Polynomial Power Method

The polynomial power method repeatedly multiplies a polynomial vector by a para-Hermitian matrix containing spectrally majorised eigenvalue to estimate the dominant eigenvector corresponding to the dominant eigenvalue. To limit the order of the resulting vector, truncation is performed in each iteration. This paper extends the polynomial power method from para-Hermitian matrices to a general polynomial matrix for determining its dominant left- and right-singular vectors and the corresponding singular value. The proposed extension assumes that the dominant singular is positive on the unit circle. The resulting algorithm is compared with a state-of-the-art PSVD algorithm and provides better accuracy with reduced computation time and lower approximation orders for the decomposition.