Perturbation Analyses for the Cholesky Factorization with Backward Rounding Errors

This paper gives perturbation analyses of the Cholesky factorization with the form of perturbations we could expect from the equivalent backward error in A resulting from numerically stable computations. The analyses more accurately reflect the sensitivity of the problem than previous such results. Both numerical results and an analysis show the standard method of symmetric pivoting usually improves the condition of the problem. It follows that the computed R will usually have more accuracy when we use the standard symmetric pivoting strategy.