Discretization of a matrix in the problem of quadratic functional binary minimization
This addresses computational bottlenecks in optimization problems for researchers in numerical methods and applied mathematics, though it appears incremental.
The paper tackles the problem of discretizing matrix elements in quadratic functional minimization with discrete coordinates, showing that optimal integer replacement procedures exist without reducing minimization efficiency. Computational complexity and RAM requirements are reduced by 16 times, with algorithm speed increased by orders of magnitude.
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.