Error estimates for the summation of real numbers with application to floating-point summation (Q2411657)

New error estimates are derived for the summation of real numbers where each sum is afflicted with some perturbation. These results improve the classical Wilkinson-type error estimates and also extend some recent results on floating-point summation. These new results are sharp, their proofs are surprisingly simple and do not make use of the particular properties of an IEEE -754 like floating-point schemes.