Verified Numerical Computations for Searching for Vectors with the Maximum Sum

Abstract

This study proposes a numerical method for searching for vectors whose sum of all elements is maximum. The vector search can be applied to many scientific problems. If we use numerical computations without considering rounding errors, in a worst-case scenario, we might find incorrect vectors as a result. We propose herein an adaptive method designed to work accurately, regardless of the rounding error problems, based on an error-free transformation of a floating-point vector.