Exploiting Symmetry in Electrical Packaging Analysis

Many properties of physical systems can be expressed by symmetric matrices of order n, where n is the number of components in the system. The computer storage requirement for inverting the most general symmetric matrix is n(n+1)/2 storage locations. For large values of n, the number of multiplications required is proportional to n
³
. If the physical system possesses certain geometrical symmetries, both the amount of storage and the number of multiplications can be reduced substantially. It will be shown that if the physical system possesses p orthogonal planes of symmetry, where p = 1, 2, or 3, and if n is sufficiently larger, then the storage requirement can be reduced approximately by 1/2
^p
and the number of multiplications by 1/4
^p
.