A Numerical Solution to KPD

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.