Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

On diakoptics: Tearing an arbitrary system


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.


References [Enhancements On Off] (What's this?)

  • [1] Gabriel Kron, Diakoptics, Macdonald, London (1963). (References to most of Kron's work can be found in this collection.)
  • [2] 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
  • [3] J. Paul Roth, An application of algebraic topology: Kron's method of tearing, Q. Appl. Math. 17(1959) 1 MR 0104337
  • [4] Alston S. Householder, A survey of some closed methods for inverting matrices, Journal SIAM 5 (1957) 3 MR 0091521
  • [5] W. R. Spillers, Network analogy for linear structures, J. Engg. Mech. Div., Proc. A.S.C.E., Aug. 1963, p. 21
  • [6] W. R. Spillers, Network techniques applied to structures, to appear in the Matrix and Tensor Quarterly


Additional Information

DOI: https://doi.org/10.1090/qam/99942
Article copyright: © Copyright 1965 American Mathematical Society

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