Neumaiersummointi
Neumaier summation is a compensated summation technique used to reduce floating-point round-off errors when summing a sequence of real numbers. The method is named after Arnold Neumaier, who contributed to numerical analysis and error-aware accumulation. Unlike naive summation, which can lose small magnitudes through cancellation, Neumaier summation maintains a running total and an auxiliary correction that tracks accumulated rounding errors. The final result is obtained by adding the correction to the running total, yielding a more accurate sum in practice.
Algorithmically, the method uses two variables: s for the running sum and c for the compensation. Initialization
Properties and usage: Neumaier summation provides improved numerical stability over naive summation and requires constant extra