Time-Variant Displacement Structure and Triangular Arrays

摘要

We extend the concept of displacement structure to time-variant matrices and useit to efficiently and recursively propagate the Cholesky factor of such matrices. A natural implementation of the algorithm is via a modular triangular array of processing elements. When the algorithm is applied to solve the normal equations that arise in adaptive least-squares filtering, we get the so-called QR algorithm, with the extra hours of a parallelizable procedure for determining the weight vector. It is shown that the general algorithm can also he implemented in time-variant lattice form: a specialization of this result yields a time-variant Schur algorithm.