{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,15]],"date-time":"2024-02-15T17:42:54Z","timestamp":1708018974313},"reference-count":15,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2006,12,19]],"date-time":"2006-12-19T00:00:00Z","timestamp":1166486400000},"content-version":"vor","delay-in-days":4431,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Circuit Theory &amp; Apps"],"published-print":{"date-parts":[[1994,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Computer\u2010aided circuit analysis is a complex procedure which may be roughly divided into three steps. the first stage is device modelling, where quantitative properties of the participating electronic devices are determined. In the second step the circuit's topology in conjunction with the device equations is exploited in order to formulate a linearized nonsingular equation set. Eventually the equation set is solved iteratively in the third phase, yielding a solution vector of circuit variables.<\/jats:p><jats:p>This paper deals with the second and third steps, where diverse sparse matrix methods are employed. Its aim is to provide a general mathematical form by which most matrix manipulation techniques can be described, thus enabling their classification on a theoretical level. Usually these methods are presented descriptively rather than strictly mathematically.<\/jats:p><jats:p>The paper introduces a matrix reduction operator from which a general matrix operator equation is deduced. This operator equation can be used to describe entire analysis approaches. After some necessary definitions, the purpose of this paper is illustrated by studying several classical examples rather than giving many mathematical proofs. the selected examples involve some well\u2010known linear equation set solution methods as well as several typical equation set transformations.<\/jats:p>","DOI":"10.1002\/cta.4490220602","type":"journal-article","created":{"date-parts":[[2007,7,2]],"date-time":"2007-07-02T11:50:07Z","timestamp":1183377007000},"page":"431-445","source":"Crossref","is-referenced-by-count":1,"title":["A general approach to circuit equations"],"prefix":"10.1002","volume":"22","author":[{"given":"T.","family":"Tuma","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F.","family":"Bratkovi\u010d","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,12,19]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCT.1971.1083223"},{"key":"e_1_2_1_3_2","volume-title":"Computer\u2010Aided Analysis of Electronic Circuits","author":"Chua L. O.","year":"1975"},{"key":"e_1_2_1_4_2","volume-title":"Memo. ERL\u2010M5520","author":"Nagel L. W.","year":"1975"},{"key":"e_1_2_1_5_2","unstructured":"M.VehovecandF.Bratkov\u010d On methods of network analysis with small number of independent variables Proc. 20th Midwest Symp. on Circuits and Systems Lubbock TX 1977 pp.340\u2013345."},{"key":"e_1_2_1_6_2","unstructured":"F.Bratkovi\u010dandT.Tuma Applicability of sparse matrix reduction to different types of circuit equations Proc. International Symposium on Networks Systems and Signal Processing\u201089 Zagreb 1989 pp.178\u2013181."},{"key":"e_1_2_1_7_2","unstructured":"T.TumaandF.Bratkovi\u010d Improved permutation and fast back substitution in sparse matrix reduction Proc. Eur. Conf. on Circuit Theory and Design\u201091 Copenhagen 1991 pp.294\u2013303."},{"key":"e_1_2_1_8_2","volume-title":"Sparse Matrices","author":"Tewarson R. P.","year":"1973"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.3.3.255"},{"key":"e_1_2_1_10_2","volume-title":"Mathematical Handbook for Scientists and Engineers","author":"Korn G. A.","year":"1961"},{"key":"e_1_2_1_11_2","volume-title":"The Algebraic Eigenvalue Problem","author":"Wilkinson J. H.","year":"1965"},{"key":"e_1_2_1_12_2","unstructured":"T. L.Quarles The Spice3 implementation guide Memo. ERL\u2010M89\/44 University of California Berkeley CA 1989."},{"key":"e_1_2_1_13_2","unstructured":"T.TumaandF.Bratkovi\u010d A mathematical model for network analysis methods Proc. Eur. Conf. on Circuit Theory and Design\u201093 Davos 1993 pp.397\u2013402."},{"key":"e_1_2_1_14_2","volume-title":"Sparse\u2010Matrizen","author":"Schendel U.","year":"1977"},{"key":"e_1_2_1_15_2","volume-title":"Applications of Matrix Theory","author":"Grover M. J. C.","year":"1989"},{"key":"e_1_2_1_16_2","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198533856.001.0001","volume-title":"The Numerical Methods Programming Projects Book","author":"Grandine T. A.","year":"1990"}],"container-title":["International Journal of Circuit Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fcta.4490220602","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/cta.4490220602","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,15]],"date-time":"2024-02-15T17:15:03Z","timestamp":1708017303000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/cta.4490220602"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,11]]},"references-count":15,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1994,11]]}},"alternative-id":["10.1002\/cta.4490220602"],"URL":"https:\/\/doi.org\/10.1002\/cta.4490220602","archive":["Portico"],"relation":{},"ISSN":["0098-9886","1097-007X"],"issn-type":[{"value":"0098-9886","type":"print"},{"value":"1097-007X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,11]]}}}