An incomplete factorization preconditioner for adaptive filtering

A method for deriving an incomplete QR factorization preconditioner for adaptive filtering is proposed. The method combines a recursive inverse QR factorization with a dropping strategy. Inverse QR factorization is more efficient compared to conventional factorization methods in that it avoids direct computation of the inverse. By realizing the factorization using a series of Givens rotation, a direct calculation of the inverse Cholesky factor is possible through the use of matrix inversion lemma and some algebraic manipulation of the Givens parameters. A dropping strategy is designed to create sparseness in the inverse Cholesky factor therefore minimizing the computational complexity of the resulting algorithm. Simulation shows that the incomplete inverse Cholesky factor derived in this paper is able to reduce the spectral condition number of the autocorrelation matrix of the problem.