Parquet Matrices and Applications

Abstract

A two-terminal network consisting of ohmic resistances can be represented ina coordinate system U,I by an oblong, the area of which is proportional to thedissipation of the whole circuit. It is filled with dissipation-rectangles of thecomponent-resistances without spaces and overlaps. A group of the twoterminalnetworks can be characterized by the so-called parquet pattern of itsrectangles-arrangement. The tension- and current-steps of the circuit of thistype can be computed by finite iteration of matrix-powers, without respectingany convergence-criteria. The method can be generalized for complicatednetworks too.