On diakoptics: Tearing an arbitrary system

Spillers, W. R.

doi:10.1090/qam/99942

Author: W. R. Spillers
Journal: Quart. Appl. Math. 23 (1965), 188-190
DOI: https://doi.org/10.1090/qam/99942
MathSciNet review: QAM99942
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Abstract | References | Additional Information

Abstract: Kron’s techniques of tearing and k-partitioning are discussed as they apply to large linear systems of an arbitrary nature and tearing is discarded as inefficient. It is shown that decreasing the size of the sub-units in k-partitioning increases its efficiency; carried to the limit, this reduction results in a Gaussian elimination scheme. Finally, the optimum application of k-partitioning is presented as a linear programming problem.

Gabriel Kron, Diakoptics, Macdonald, London (1963). (References to most of Kron’s work can be found in this collection.)

Franklin H. Branin, The relation between Kron’s method and the classical methods of network analysis, IRE WESCON Convention Record, Part 2, 1959, pp. 1-29

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
Alston S. Householder, A survey of some closed methods for inverting matrices, J. Soc. Indust. Appl. Math. 5 (1957), 155–169. MR 91521

W. R. Spillers, Network analogy for linear structures, J. Engg. Mech. Div., Proc. A.S.C.E., Aug. 1963, p. 21

W. R. Spillers, Network techniques applied to structures, to appear in the Matrix and Tensor Quarterly