A technique is described which allows least squares computation to be made at arbitrarily high sampling rates, overcoming the inherent speed limitation due to the recursive algorithms. Previous efforts at high sampling rate systolic implementations of least squares problems have used Givens transformations and QR decomposition, achieving a sampling rate limited by the time required by several multiplication operations. Taking advantage of the linearity of the least squares recursion, the algorithms can be recast into a new realization for which the bound on throughput of least squares computation is arbitrarily high. The technique, which has previously been applied to adaptive lattice filters, is shown to be applicable to the matrix triangularization related problems such as solving general linear systems and computing eigenvalues by the QR algorithm.