Systematic Scaling for Digital Differential Analyzers

The usefulness of large-capacity digital differential analyzers (DDA´s) is severely hampered by the complexity of the scaling process. The scales needed for programming a DDA have to be compatible with the so-called ``equilibrium,´´ ``topological,´´ and ``boundary´´ constraints, imposed by the construction of the analyzer and the nature of the problem at hand. Simultaneous trial-and-error satisfaction of all these constraints, to achieve optimal range and accuracy of computation, is practically impossible for any problem involving more than a few integrators. The paper shows how the scaling constraints can be organized in a matrix form, and how optimal scales can be produced in a systematic manner. The proposed scheme, which can be programmed for automatic execution, is adaptable for DDA´s operating in conjunction with general-purpose digital computers.