{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,5]],"date-time":"2026-04-05T06:40:41Z","timestamp":1775371241943,"version":"3.50.1"},"reference-count":18,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2007,9,5]],"date-time":"2007-09-05T00:00:00Z","timestamp":1188950400000},"content-version":"vor","delay-in-days":8282,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems &amp; Computers in Japan"],"published-print":{"date-parts":[[1985,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Diakoptics is a kind of hybrid analysis. It has a problem wherein the calculation of the inverse of the admittance sparse submatrix for the subnetwork produces a non\u2010sparse impedance submatrix and the sparsity of the submatrix is not utilized effectively for a large\u2010scale network. From such a viewpoint, tearing methods have recently been proposed which consider the sparsity of sub\u2010matrices. In the methods proposed till now, however, a complex sparsity technique is required for the processing of submatrices, which is different from the tearing algoriithm. For these kinds of algorithms, the computational complexity is difficult to evaluate, and the optimal tearing based on evaluation has not been considered. This paper avoids the hybrid analysis and proposes a method of network analysis which provides a nonsingular hierarchical tearing of subnetworks so that the decomposed sub\u2010matrix is always of admittance type. As a result, the node conductance matrix is of a block diagonal structure with bordered block\u2010diagonal matrices as the blocks. By iterating the hierarchical tearing, each block is reduced further to the bordered block\u2010diagonal structure with denser sub\u2010matrices as blocks. By this method, the preprocessing of tearing and LU decomposition can be separated, making the sparsity technique of the submatrices unnecessary. Based on the evaluation of the computational complexity, almost optimal tearing can be performed.<\/jats:p>","DOI":"10.1002\/scj.4690160607","type":"journal-article","created":{"date-parts":[[2007,7,7]],"date-time":"2007-07-07T10:22:58Z","timestamp":1183803778000},"page":"59-67","source":"Crossref","is-referenced-by-count":2,"title":["Network analysis by hierarchical tearing method"],"prefix":"10.1002","volume":"16","author":[{"given":"Hideki","family":"Asai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shinsaku","family":"Mori","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2007,9,5]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.1721447"},{"key":"e_1_2_1_3_2","unstructured":"S.Amari.Topological foundations of Kron's tearing of electric networks: Information\u2010theoretical foundations of diakoptics and codiakoptics RAAG Memoirs 3 F \u2010 VI; F \u2010 VII pp.322\u2013350 351\u2013371(1962)."},{"key":"e_1_2_1_4_2","unstructured":"M.IriandT.Sunaga.A comment on the efficacy of diakoptical analysis from an information\u2010theoretical viewpoint RAAG Memoirs 2 F \u2010 IV pp.404\u2013408(1958)."},{"key":"e_1_2_1_5_2","first-page":"140","volume-title":"Basic Theory of Electrical Networks","author":"Ondera R.","year":"1967"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/PROC.1974.9545"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1976.1084166"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1980.1084825"},{"key":"e_1_2_1_9_2","first-page":"643","volume-title":"A hierarchical decomposition approach for network analysis","author":"Gupta H.","year":"1982"},{"key":"e_1_2_1_10_2","first-page":"427","volume-title":"LU decomposition and forward\u2010backward substitution of recursive bordered block diagonal matrices","author":"Vlach M.","year":"1983"},{"key":"e_1_2_1_11_2","volume-title":"VLSI systems and compositions","author":"Rung H. T.","year":"1981"},{"issue":"12","key":"e_1_2_1_12_2","first-page":"1416","article-title":"Bit\u2010serial LU decomposition processor","volume":"66","author":"Shlmizu N.","year":"1983","journal-title":"Trans. (D) I.E.C.E., Japan"},{"key":"e_1_2_1_13_2","volume-title":"Diakoptics: Multilevel tearing method and estimation of the computation time","author":"Asai H.","year":"1984"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1109\/TC.1982.1675979"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1975.1084003"},{"issue":"2","key":"e_1_2_1_16_2","article-title":"Extension of diakoptics and its application to non\u2010singular decomposition of network","volume":"102","author":"Fukao T.","year":"1982","journal-title":"Trans. (C), I.E.E., Japan"},{"issue":"1","key":"e_1_2_1_17_2","first-page":"97","article-title":"Network analysis by modified diakoptics and optimal number of decompositions","volume":"66","author":"Asai H.","year":"1984","journal-title":"Trans. (D), I.E.C.E., Japan"},{"key":"e_1_2_1_18_2","unstructured":"G.D.Hatchtel.Design techniques in the third generation network simulator (1) Nikkei Electronics p.156(1982)."},{"issue":"12","key":"e_1_2_1_19_2","first-page":"1467","article-title":"A computer for symbolic analysis of linear active networks based on two\u2010graph method \u2013 tree generator \u2013","volume":"65","author":"Tanaka M.","year":"1982","journal-title":"Trans. (D)"}],"container-title":["Systems and Computers in Japan"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fscj.4690160607","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/scj.4690160607","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T18:20:26Z","timestamp":1697826026000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/scj.4690160607"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1985,1]]},"references-count":18,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1985,1]]}},"alternative-id":["10.1002\/scj.4690160607"],"URL":"https:\/\/doi.org\/10.1002\/scj.4690160607","archive":["Portico"],"relation":{},"ISSN":["0882-1666","1520-684X"],"issn-type":[{"value":"0882-1666","type":"print"},{"value":"1520-684X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1985,1]]}}}