Inverse updating and downdating for weighted linear least squares using M-invariant reflections Original Research Article

A new method for the weighted linear least squares problem min ydouble vertical barM1/2(b−Ax)double vertical bar2 is presented by introducing a row M-invariant matrix (i.e., QMQT = M). Our purpose in this paper is to introduce new row M-invariant and row hyperbolic M-invariant reflections. We then show how these row M-invariant reflections can be used to design efficient sliding-date-window recursive weighted linear least squares covariance algorithms, which are based upon rank-k modifications to the inverse like-Cholesky factor R−1 of the covariance matrix. The algorithms are rich in matrix-matrix BLAS-3 computations. We also provide computational experiments indicating the numerical stability of the methods.