A Numerical Solution to KPD

TL;DR

This paper introduces a stationary value based algorithm (SVA) for solving the nearest Kronecker product decomposition (KPD) problem in hypermatrices, applicable to both vector and matrix forms, with demonstrated numerical effectiveness.

Contribution

The paper presents a novel SVA algorithm for KPD of hypermatrices, including a method to convert matrix form to vector form using permutation matrices, expanding the applicability of existing algorithms.

Findings

The SVA effectively solves the KPD problem for hypermatrices.

Numerical examples show the algorithm's competitive performance.

The method extends to finite sum KPD and matrix form hypermatrices.

Abstract

A stationary value based algorithm (SVA) is provided to solve the nearest Kronecker product decomposition (KPD) problem of vector form hypermatrices. Using the algorithm successively, the finite sum KPD is also solved. Then the permutation matrix is introduced. Using it, the KPD of matrix form hypermatrices is converted to its equivalent KPD of vector forms, and then the SVA is also applicable to solve the same problems for vector form hypermatrix. Some numerical examples are presented to demonstrate the new algorithm and to compare it with existing methods.