Summation Problem Revisited -- More Robust Computation

TL;DR

This paper introduces a simple, efficient summation algorithm suitable for large datasets, improving numerical accuracy and computational efficiency over existing methods, especially when summing values with large exponent differences.

Contribution

It proposes a practical, easy-to-implement summation algorithm with linear complexity, outperforming the quadratic-time ESSA in handling large and diverse data sets.

Findings

Algorithm has O(N) complexity, faster than ESSA

Provides more accurate summation with large exponent differences

Suitable for medium and large data sets with small and large values

Abstract

Numerical data processing is a key task across different fields of computer technology use. However, even simple summation of values is not precise due to the floating point representation use. This paper presents a practical algorithm for summation of values convenient for medium and large data sets. The proposed algorithm is simple, easy to implement. Its computational complexity is O(N) in the contrary of the Exact Sign Summation Algorithm (ESSA) approach with O(N^2) run-time complexity. The proposed algorithm is especially convenient for cases when exponent data differ significantly and many small values are summed with higher values