The Kron method of tearing and the dual method of identification

Weinzweig, A. I.

doi:10.1090/qam/112587

Author: A. I. Weinzweig
Journal: Quart. Appl. Math. 18 (1960), 183-190
MSC: Primary 78.00; Secondary 15.00
DOI: https://doi.org/10.1090/qam/112587
MathSciNet review: 112587
Full-text PDF Free Access

Beno Eckmann, Harmonische Funktionen und Randwertaufgaben in einem Komplex, Comment. Math. Helv. 17 (1945), 240–255 (German). MR 13318, DOI https://doi.org/10.1007/BF02566245

G. Kron, Tensor analysis of networks, John Wiley and Sons, New York, 1939

Gabriel Kron, A set of principles to interconnect the solutions of physical systems, J. Appl. Phys. 24 (1953), 965–980. MR 60913
Gabriel Kron, A method of solving very large physical systems in easy stages, Proc. I.R.E. 42 (1954), 680–686. MR 60305

G. Kron, Solving highly complex elastic structures in easy stages, J. Appl. Mechanics, Paper No. 54–A–25

Gabriel Kron, Detailed example of interconnecting piecewise solutions, J. Franklin Inst. 259 (1955), 307–333. MR 68320, DOI https://doi.org/10.1016/0016-0032%2855%2990641-4
Gabriel Kron, Tearing and interconnecting as a form of transformation, Quart. Appl. Math. 13 (1955), 147–159. MR 73431, DOI https://doi.org/10.1090/S0033-569X-1955-73431-7

P. LeCorbeiller, Matrix analysis of electrical networks, Harvard University Press, 1950

J. C. Maxwell, Electricity and magnetism, Clarendon Press, Oxford, 1873

J. P. Roth, An application of algebraic topology to numerical analysis: on the existence of a solution to the network problem, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 518–521. MR 74094, DOI https://doi.org/10.1073/pnas.41.7.518
J. P. Roth, The validity of Kron’s method of tearing, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 599–600. MR 74095, DOI https://doi.org/10.1073/pnas.41.8.599
J. Paul Roth, An application of algebraic topology: Kron’s method of tearing, Quart. Appl. Math. 17 (1959), 1–24. MR 104337, DOI https://doi.org/10.1090/S0033-569X-1959-0104337-1

A. I. Weinzweig, Topology and network theory, in preparation