%0 Journal Article %1 Honnell1968Krons %A Honnell, Pierre M. %D 1968 %J Journal of the Franklin Institute %K 94c05-analytic-circuit-theory 94c15-circuits-networks-applications-of-graph-theory kron %N 6 %P 566--571 %R 10.1016/0016-0032(68)90394-3 %T Kron's Methods and the Theoretical Foundation of the Matric Computor %U http://dx.doi.org/10.1016/0016-0032(68)90394-3 %V 286 %X Kron's fundamental approach to the theory of electric networks, symbolized by the famous formula I′ = AtYpAE′, applies equally well to electronic networks. In particular, the fundamental theory of The Matric Computor—an analytic machine for the solution of problems such as arise in the applications of Kron's theories—is shown to follow from a generalized version of this formula, followed by employment of the reduction formula for the suppression of superfluous machine coordinates. This establishes the homeomorphism between the electronics and the mathematics, j=Yv↷b=Ax, in which the entries in the matrices are real numbers, derivative coefficients, and linear functionals. The response vector v↷x is automatically generated and yields the solutions of algebraic and integro-differential matric equation systems, linear or nonlinear.

@article{Honnell1968Krons, abstract = {{Kron's fundamental approach to the theory of electric networks, symbolized by the famous formula I′ = AtYpAE′, applies equally well to electronic networks. In particular, the fundamental theory of The Matric Computor—an analytic machine for the solution of problems such as arise in the applications of Kron's theories—is shown to follow from a generalized version of this formula, followed by employment of the reduction formula for the suppression of superfluous machine coordinates. This establishes the homeomorphism between the electronics and the mathematics, j]=[Y]v]↷b]=[A]x], in which the entries in the matrices are real numbers, derivative coefficients, and linear functionals. The response vector v]↷x] is automatically generated and yields the solutions of algebraic and integro-differential matric equation systems, linear or nonlinear.}}, added-at = {2019-03-01T00:11:50.000+0100}, author = {Honnell, Pierre M.}, biburl = {https://www.bibsonomy.org/bibtex/234dd1edd013550105b91803e7390883d/gdmcbain}, citeulike-article-id = {14612837}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/0016-0032(68)90394-3}, doi = {10.1016/0016-0032(68)90394-3}, interhash = {ae9f42d7df2bd1384dd02e2788f4b801}, intrahash = {34dd1edd013550105b91803e7390883d}, issn = {00160032}, journal = {Journal of the Franklin Institute}, keywords = {94c05-analytic-circuit-theory 94c15-circuits-networks-applications-of-graph-theory kron}, month = dec, number = 6, pages = {566--571}, posted-at = {2018-07-10 03:13:17}, priority = {2}, timestamp = {2019-03-01T00:11:50.000+0100}, title = {Kron's Methods and the Theoretical Foundation of the {M}atric {C}omputor}, url = {http://dx.doi.org/10.1016/0016-0032(68)90394-3}, volume = 286, year = 1968 }