BLOCK RLS USING ROW HOUSEHOLDER REFLECTIONS

Householder reflections applied from the left are generally used to ze ro a contiguous sequence of entries in a column of a matrix A. Our pur pose in this paper is to introduce new row Householder and row hyperbo lic Householder reflections which are also applied from the left, but now zero a contiguous sequence of entries in a row of A. We then show how these row Householder reflections can be used to design efficient sliding-data-window recursive least-squares (RLS) covariance algorithm s, which are based upon rank-k modifications to the inverse Cholesky f actor R-1 of the covariance matrix. The algorithms are rich in matrix- matrix BLAS-3 computations, making them efficient on vector and parall el architectures. Preliminary numerical experiments are reported, comp aring these row Householder-based rank-k modification schemes with k a pplications of the classical updating and downdating covariance scheme s which use Givens and hyperbolic rotations.