Numerical and Algebraic Generation of Mesh-Impedance Matrices by Set-Theoretical Intersection on a Digital Computer

The mesh-impedance matrix Z
⁰
and, in dual correspondence, the cut-set admittance matrix Y
^ø
, are usually generated by the product C
_ɩ
ZC or HYH
_t
, respectively, so that two matrix multiplications must be carried out in each case. By use of certain topological relationships and of the fact that the transforming matrices are incidence matrices where only +1, -1, or 0 can appear as elements, a set-theoretical rule can be stated for the generation of these matrices. The rule increases by a factor of 7 to 8 the speed with which such matrices can be produced on a digital computer. By virtue of the existence of the mesh-mesh and cut-set-cut-set incidence matrices-a condition which will be proved-the mesh-impedance matrices Z
⁰
and cut-set admittance matrices Y
⁰
can also be generated algebraically. (An extension of the method described here was developed by the author under the title, ``Arithmetik verdichtet gespeicherter Inzidenzvektoren, welche die Topologie von Netzen darstellen,'' and was published in Berlin, Germany, by Zeitschrift fur Angewandte Mathematik und Mechanik, vol. 43, Dec. 1963, pp. T9-T12.)