Kron's method for symmetric eigenvalue problems (Q1298806)

\textit{G. Kron's} method [Drakoptics. Macdonald, London (1963)] has been used by engineers for over 30 years to calculate eigenvalues of large scale matrices \(A\) exhibiting special block structures. The method consists, roughly speaking, in eliminating part of the variables \(x_1,\dots, x_n\) occuring in the system \((A-\lambda I)x= 0\) and treating numerically the resulting Kron matrix of smaller dimension. The present author considers the symmetric matrix eigenvalue problem resulting from the discretization of a selfadjoint differential operator on a domain consisting of non-overlapping subdomains. Here, the dimension of the Kron matrix equals to the number of unknowns on the interfaces. The paper presents a self-contained theoretical treatment of the zeroes and poles of the Kron matrix and their relationships with the eigenvalues of the original matrix.