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 n3. 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 1/2p and the number of multiplications by 1/4p.

A model based on network theory is presented for calculating the frequency-dependent resistance and inductance per unit length matrices for transmission line systems consisting of conductors with rectangular cross sections. The calculated results are compared with actual measurements. Excellent agreement is obtained over a wide range of frequencies, including the mid-range where neither dc values nor high-frequency limit values apply.

The advanced statistical analysis program (ASTAP) is a general-purpose network-analysis program which performs nonlinear transient, dc, and ac analyses and provides statistical simulation to determine the distribution of circuit outputs due to parameter variations. The program combines a user-oriented input language capable of describing completely general nonlinear devices with the latest advances in numerical and programming techniques: variable-order implicit integration, tableau formulation, and sparse-matrix solution methods. This paper describes how these techniques have been implemented in the ASTAP program. Attention is focused on the computational algorithms.

Starting with Maxwell's equations, the transmission line equations are derived for a system consisting of an arbitrary number of conductors. The derivation is rigorous for long lossless conductors embedded in a uniform perfect dielectric. The presentation is essentially tutorial, most of the results being well known, at least for two- and three-conductor systems. The novelty lies in the point of view adopted in obtaining a systematic generalization to the case of an arbitrary number of conductors. Explicit expressions are obtained for the electric and magnetic fields in the dielectric surrounding the conductors, and a rigorous formulation is given for the problem of calculating the coefficients of capacitance and inductance.