## Adam Florence

Research

Nearest Inverse Kronecker Product

The nearest inverse Kronecker product problem is: Given the
*m*-by-*m*_{X} *m*_{Y} matrix *A*,
and the *m*-by-*n*_{X} *n*_{Y} matrix
*B*, find the
*m*_{X}-by-*n*_{X} matrix *X* and the
*m*_{Y}-by-*n*_{Y} matrix *Y* which minimize
|| B - A ( X `kron` Y ) ||_{2}
Assume without loss of generality that || *X* ||_{F} = 1.
If *A* is square and *B* is the identity, then the problem
becomes finding the Kronecker product closest to the inverse of
*A*.

We have developed several algorithms to solve this problem. They are
explained in [1]. The
Matlab code is:

**There is no warranty of any kind on this code or its documentation.**
All code is copyrighted (c) 2000, 2001 by Adam Florence.
If you have any questions about the code, please
e-mail me.

**Bibliography**
- FLORENCE, ADAM G.
*Computational Multilinear Algebra*, Ph.D. dissertation, Cornell
University, 2001.

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*Last updated 13 August 2001.*