Y-MP floating point and Cholesky factorization

Abstract

The floating point arithmetics implemented in the Cray 2 and Cray Y-MP computer systems are nearly identical, but large scale computations performed on the two systems have exhibited significant differences in accuracy. The difference in accuracy is analyzed for Cholesky factorization algorithm, and it is found that the source of the difference is the subtract magnitude operation of the Cray Y-MP. The results from numerical experiments for a range of problem sizes are presented, and an efficient method for improving the accuracy of the factorization obtained on the Y-MP is presented.