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In systems analysis, Diakoptics (Greek ''dia''–through + ''kopto''–cut,tear) or the "Method of Tearing" involves breaking a (usually physical) problem down into subproblems which can be solved independently before being joined back together to obtain an ''exact'' solution to the whole problem. The term was introduced by Gabriel Kron in a series "Diakoptics — The Piecewise Solution of Large-Scale Systems" published in London, England by ''The Electrical Journal'' between June 7, 1957 and February 1959. The twenty-one installments were collected and published as a book of the same title in 1963. The term ''diakoptics'' was coined by Philip Stanley of the Union College Department of Philosophy.〔Kron 1963 p 1〕 ==Features== According to Kron, "Diakoptics, or the Method of Tearing, is a combined theory of a pair of storehouses of information, namely equations+graph, or matrices+graph, associated with a given physical or economic system.".〔Kron 1963 p 1〕 What Kron was saying here is that in order to carry out the Method of Tearing, not only were the system equations needed, but also the topology of the system. Diakoptics was explained in terms of algebraic topology by J. Paul Roth.〔J.P. Roth (1959) "An application of algebraic topology to numerical analysis: On the existence of a solution to the network problem", Proceedings of the National Academy of Sciences of the United States of America 41(7):518–21 〕〔J.P. Roth (1959) "The validity of Kron’s method of tearing", ''PNAS'' 41(8):599–600 〕〔Paul J. Roth (1959) "An application of algebraic topology: Kron’s method of tearing", ''Quarterly of Applied Mathematics'' 17:1–24〕 Roth describes how Kirchhoff's circuit laws in an electrical network with a given impedance matrix or admittance matrix can be solved for currents and voltages by using the circuit topology. Roth translates Kron’s "orthogonality conditions" into exact sequences of homology or cohomology. Roth’s interpretation is confirmed by Raoul Bott in reports in Mathematical Reviews. Roth says, "tearing consists essentially in deducing from the solution of one (easier to solve) network K~ the solution of a network K having the same number of branches as K~ and having the same isomorphism L between the groups of 1-chains and 1-cochains." Diakoptics can be seen applied for instance in the text ''Solution of Large Networks by Matrix Methods''.〔Homer E. Brown (1974, 1985) ''Solution of Large Networks by Matrix Methods'', John Wiley & Sons ISBN 0-471-80074-0〕 Diakoptics is peculiar as a decomposition method, in that it involves taking values on the "intersection layer" (the boundary between subsystems) into account. The method has been rediscovered by the parallel processing community under the name "Domain Decomposition".〔Lai C. H. (1994) "Diakoptics, Domain Decomposition and Parallel Computing", The Computer Journal, Vol 37, No 10, pp. 840–846〕 According to Keith Bowden, "Kron was undoubtedly searching for an ontology of engineering".〔K. Bowden (1998) "Physical computation and parallelism (constructive postmodern physics)", International Journal of General Systems 27(1–3):93–103〕 Bowden also described "a multilevel hierarchical version of the method, in which the subsystems are recursively torn into subsubsystems".〔K. Bowden (1991) "Hierarchical Tearing: An Efficient Holographic Algorithm for System Decomposition", ''International Journal of General Systems'' 24(1), pp 23–38〕 When parallel computing was provided by the transputer, Keith Bowden described how diakoptics might be applied.〔K. Bowden (1990) "Kron's Method of Tearing on a Transputer Array", ''The Computer Journal'' 33(5):453–459〕 It is an ongoing open question how the parallelism of Quantum Computing may be relevant. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Diakoptics」の詳細全文を読む スポンサード リンク
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