A Numerical Solution to KPD
This work addresses a computational linear algebra problem for researchers in numerical methods, but it appears incremental as it builds on existing KPD techniques.
The authors tackled the nearest Kronecker product decomposition (KPD) problem for hypermatrices by proposing a stationary value based algorithm (SVA) that handles vector forms, extends to finite sums, and adapts to matrix forms via permutation matrices, with numerical examples demonstrating its performance compared to existing methods.
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.