In recent studies operator factorization techniques have been developed for problems associated with multidimensional control and image processing. In particular the “special factorization” of Gohberg and Krein and the Schur-Coleski factorization have both been extended to the multivariate setting. The present study focuses on computational aspects of the earlier results. Also of interest are implications for designing computer architectures which facilitate high-speed, online computation of the operator factors.