An Algorithm for Computing the QR Decomposition of a Polynomial Matrix

This paper introduces an algorithm for computing a QR decomposition of a polynomial matrix. The algorithm proceeds to perform the decomposition by following the same strategy in eliminating entries of the matrix as is used in the Givens method for a QR decomposition of a scalar matrix. However scalar Givens rotation matrices can no longer be applied. Instead, a polynomial Givens rotation is introduced, enabling the QR decomposition of a polynomial matrix. Convergence of the algorithm is discussed and through simulations the capability of the algorithm is assessed.