TIME-VARIANT DISPLACEMENT STRUCTURE AND TRIANGULAR ARRAYS

We extend the concept of displacement structure to time-variant matric es and use it to efficiently and recursively propagate the Cholesky fa ctor of such matrices. A natural implementation of the algorithm is vi a a modular triangular array of processing elements. When the algorith m is applied to solve the normal equations that arise in adaptive leas t-squares filtering, we get the so-called QR algorithm, with the extra bonus of a parallelizable procedure for determining the weight vector . It is shown that the general algorithm can also be implemented in ti me-variant lattice form; a specialization of this result yields a time -variant Schur algorithm.