Kronecker polynomials and their applications

Kronecker products of matrices arise in a wide variety of applications and have been exploited in numerous algorithms to significantly reduce operation counts. In the present paper, simple (left and right) Kronecker polynomials are defined and a method is presented for calculating their spectral decomposition. The procedure is illustrated on block tridiagonal matrices and on block matrices with circulant blocks. Double Kronecker polynomials are defined as well and their spectral properties are given. The results can be applied for solving the discrete Poisson equation in two- and three-dimensional cases. © 1999 Elsevier Science Ltd. All rights reserved.