Preconditioned conjugate gradient methods for adaptive filtering

The method of preconditioned conjugate gradients (PCGs) is proposed for solving the problem of adaptive filtering. Considered as an iterative algorithm, the PCG algorithm is asymptotically efficient. It is suggested for use in applications requiring very high order adaptive filters. The method is also extended to the IIR (infinite impulse response) case. Application of the PCG algorithm to very long filters is suggested to exploit the fact that the number of iterations of the PCG algorithm until convergence is independent of the filter order. In a block algorithm, then, increasing filter length increases the efficiency of the algorithm.