Discretization of a matrix in the problem of quadratic functional binary minimization

TL;DR

This paper investigates discretizing matrix elements in quadratic functional minimization problems, showing an optimal integer replacement method that maintains efficiency and significantly reduces computational complexity.

Contribution

It introduces an optimal procedure for discretizing matrix elements in quadratic minimization, preserving minimization quality and improving computational efficiency.

Findings

Optimal integer replacement procedure exists for matrix discretization.

Computational complexities and RAM requirements are reduced by 16 times.

Using integer elements increases minimization algorithm speed significantly.

Abstract

The capability of discretization of matrix elements in the problem of quadratic functional minimization with linear member built on matrix in N-dimensional configuration space with discrete coordinates is researched. It is shown, that optimal procedure of replacement matrix elements by the integer quantities with the limited number of gradations exist, and the efficient of minimization does not reduce. Parameter depends on matrix properties, which allows estimate the capability of using described procedure for given type of matrix, is found. Computational complexities of algorithm and RAM requirements are reduced by 16 times, correct using of integer elements allows increase minimization algorithm speed by the orders.