Parallel windowed block recursive least squares

We report results on the parallel implementation of accurate algorithms for the windowed recursive least squares (WRLS) problem. In this problem both updating and downdating of matrix factorizations takes place, where in either case, the factorization is modified by a block of rows. We consider two algorithms, block Gram-Schmidt with re-orthogonalization (BGSR) (S.J. Olszanskyj et al.) and corrected semi-normal equations (CSNE) (L. Elden, H. Park, 1992). We implemented the algorithms for the Intel iPSC/860 Hypercube and Intel Paragon XP/S architectures. Test results show that even though the BGSR algorithm has more work to do, it exhibits better scaled speedup and is in many scenarios faster than CSNE in parallel