Kronʹs method for symmetric eigenvalue problems

Kronʹs method has been used successfully by engineers for over 30 years to find eigenvalues of large symmetric matrices. These matrices arise from domain decomposition of nonoverlapping domains of self-adjoint partial differential operators. This paper discusses some theoretical aspects of Kronʹs method. Specifically, the poles and zeroes of eigenvalues of the Kron matrix and their relationships with the eigenvalues of the original matrix are given.