Block RLS using row Householder reflections (Q1260781)

The authors introduce new row Householder and row hyperbolic Householder reflections to zero a contiguous sequence of entries in a row of a matrix when applied from the left. These reflections are used to develop efficient algorithms for recursive least squares (RLS) problems of the sliding window type. These algorithms are based upon rank-\(k\) modification to the inverse Cholesky factor \(R^{-1}\) of the covariance matrix. Numerical experiments show that these algorithms are rich in matrix- matrix BLAS-3 computations, making them even more economical on high performance architectures than \(k\) applications of rank-1 modification schemes.