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 operatio n counts. In the present paper, simple (left and right) Kronecker polynomia ls are defined and a method is presented for calculating their spectral dec omposition. The procedure is illustrated on block tridiagonal matrices and on block matrices with circulant blocks. Double Kronecker polynomials are d efined as well and their spectral properties are given. The results can be applied for solving the discrete Poisson equation in two- and three-dimensi onal cases. (C) 1999 Elsevier Science Ltd. All rights reserved.