A QR algorithm was designed using sparse matrix techniques for likelihood evaluation in REML. The efficiency of the algorithm depends on how the order of columns in the mixed model array are arranged. Three heuristic orderings were considered. The QR algorithm was tested successfully in likelihood evaluation, but vector processing was needed to finish the procedure because of excess fill-ins. The improvements made for the QR algorithm also applied to the competing absorption approach, and hence absorption was found to be more competitive than the QR algorithm in terms of computing time and memory requirements. Absorption was made 52 times faster than a first generation absorption algorithm.
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