A method for partitioning a high order matrix into blocks in order to find its eigenvalues

To save time and space in a computer a method is derived of partitioning high-order and infinite matrices in such a way that their eigenvalues can be found. This method is iterative, and determines an eigenvalue approximately by introducing corrections to an eigenvalue of the truncated matrix.
The matrix considered is taken to be symmetric. Comparisons are made between the eigenvalues of $A$ and of $\overline A$, matrix of the same order as the truncation of $A$, and derived from its blocks. A measure of the convergence of the iteration process is found.