Reduction of functions of some partitioned matrices

Abstract

In the numerical analysis of physical problems, there often arise large matrices which exhibit certain kinds of block-symmetry when partitioned appropriately. In this article, the structures of the frequently-occurring hyper-circulant and hyper-Jacobi matrices are examined, and it is shown how the calculation of any analytic function of such matrices may be reduced to the calculation of functions of the submatrices. Examples drawn from current engineering literature are given as well as small illustrative examples.