The most efficient implementation of the IQML algorithm

The work by Clark and Scharf (1992) showed a new implementation of the IQML (iterative quadratic maximum likelihood) algorithm, which requires at each iteration computational flops of order N² where N is the dimension of signal vector (or length of data sequence). They also indicated that the implementation of other related algorithms such as the Steiglitz-McBride (1965) algorithm would also require order N² computations. The present author gives a better way of implementation which requires computational flops of the order N. This better way of implementation is shown in detail for the IQML algorithm. Following the same idea shown in the present paper, one can also straightforwardly design the order N implementation of the Steiglitz-McBride algorithm. The present implementation is also the most efficient in that no implementation can be made less than order N²