Preprocessed Cholesky-Factor Downdatings for Observation Matrices

This paper introduces PGD(Preprocessed Givens Downdating)and PHD(Preprocessed Hyperbolic Downdating) algorithms, wherein a multiple-row observation matrix is factorized into a partial Cholesky factor Rz, such that = , and then Rz is recursively downdated by using GD(Givens Downdating)and HD(Hyperbolic Dondating), respectively. Time complexities of PGD and PHD algorithms are ＋ 및 ＋ flops, respectively, if pn, while those of the existing GD and HD are known to be and flops,, respectively. This concludes that the factorization of observation matrices, which we call preprocessing, would improve the overall performance of the downdating process. Benchmarks on the Sun SPARC/2 system also show that preprocessing would shorten the required downdating times compared to those of downdatings without preprocessing. Furthermore, benchmarks also show that PHD provides better performance than PGD