Binary Solutions for Overdetermined Systems of Linear Equations

TL;DR

This paper introduces a finite step method combining dynamic programming and branch-and-bound techniques to efficiently compute binary solutions for overdetermined linear systems, demonstrated through numerical examples.

Contribution

It presents a novel finite step approach for binary solutions in overdetermined systems using dynamic programming and branch-and-bound, enhancing computational efficiency.

Findings

Method successfully computes binary solutions in finite steps

Numerical examples validate the effectiveness of the approach

Approach improves computational efficiency over existing methods

Abstract

This paper presents a finite step method for computing the binary solution to an overdetermined system of linear algebraic equations Ax = b, where A is an m x n real matrix of rank n < m, and b is a real m-vector. The method uses the optimal policy of dynamic programming along with the branch and bound concept. Numerical examples are given.