A modification to the linpack downdating algorithm

Alinpack downdating algorithm is being modified by interleaving its two different phases, the forward solving a triangular system and the backward sweep of Givens rotations, to yield a new forward method for finding the Cholesky decomposition ofR ^T R –zz ^T . By showing that the new algorithm saves forty percent purely redundant operations of the original, better stability properties are expected. In addition, various other downdating algorithms are rederived and analyzed under a uniform framework.