{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T01:23:13Z","timestamp":1790644993936,"version":"4.1.0"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2007,1]]},"abstract":"<jats:p>We describe a fill\u2010reducing ordering algorithm for sparse, nonsymmetric LU factorizations, where the pivots are restricted to the diagonal and are selected greedily. The ordering algorithm uses only the structural information. Most of the existing methods are based on some type of symmetrization of the original matrix. Our algorithm exploits the nonsymmetric structure of the given matrix as much as possible. The new algorithm is thus more complex than classical symmetric orderings, but we show that our algorithm can be implemented in space bounded by the number of nonzero entries in the original matrix, and has the same time complexity as the analogous algorithms for symmetric matrices. We provide numerical experiments to demonstrate the ordering quality and the runtime of the new ordering algorithm.<\/jats:p>","DOI":"10.1137\/050637315","type":"journal-article","created":{"date-parts":[[2007,1,18]],"date-time":"2007-01-18T09:40:41Z","timestamp":1169113241000},"page":"228-244","source":"Crossref","is-referenced-by-count":10,"title":["Diagonal Markowitz Scheme with Local Symmetrization"],"prefix":"10.1137","volume":"29","author":[{"given":"Patrick R.","family":"Amestoy","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoye S.","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Esmond G.","family":"Ng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2007,1,12]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479894278952"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1177\/109434208900300303"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1145\/504210.504212"},{"key":"R4","unstructured":"P. R. Amestoy, X. S. Li, and E. G. Ng,\n                      Diagonal Markowitz Scheme with Local Symmetrization\n                      , Technical report LBNL\u201053854, Lawrence Berkeley National Laboratory, Berkeley, CA, 2003; also appeared as ENSEEIHT\u2010IRIT report RT\/APO\/03\/05."},{"key":"R5","unstructured":"P. R. Amestoy, X. S. Li, and S. Pralet,\n                      Unsymmetric ordering using a constrained Markowitz scheme\n                      , SIAM J. Matrix Anal. Appl., to appear."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479800375370"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1145\/992200.992205"},{"key":"R8","unstructured":"I. S. Duff, R. G. Grimes, and J. G. Lewis,\n                      The Rutherford\u2010Boeing Sparse Matrix Collection\n                      , Technical report RAL\u2010TR\u201097\u2010031, Rutherford Appleton Laboratory, Didcot, UK, 1997; also Technical report ISSTECH\u201097\u2010017 from Boeing Information & Support Services and Report TR\/PA\/97\/36 from CERFACS, Toulouse; http:\/\/www.cse.clrc.ac.uk\/Activity\/SparseMatrices\/."},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479897317661"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479899358443"},{"key":"R11","unstructured":"I. S. Duff, A. M. Erisman, and J. K. Reid,\n                      Direct Methods for Sparse Matrices\n                      , Oxford University Press, Oxford, UK, 1987."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1145\/356044.356047"},{"key":"R13","unstructured":"A. George and J. W. H. Liu,\n                      Computer Solution of Large Sparse Positive Definite Systems\n                      , Prentice\u2013Hall, Englewood Cliffs, NJ, 1981."},{"key":"R14","unstructured":"K. Goto,\n                      High\u2010Performance BLAS\n                      , http:\/\/www.cs.utexas.edu\/users\/flame\/goto\/."},{"key":"R15","unstructured":"HSL,\n                      A Collection of Fortran Codes for Large Scale Scientific Computation\n                      , http:\/\/www.cse.clrc.ac.uk\/Activity\/HSL (2000)."},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1145\/779359.779361"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1145\/214392.214398"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1137\/0611010"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.3.3.255"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479897319313"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(94)00192-8"},{"key":"R22","doi-asserted-by":"crossref","unstructured":"G. Pagallo and C. Maulino,\n                      A bipartite quotient graph model for unsymmetric matrices\n                      , in Numerical Methods, Lecture Notes in Math. 1005, Springer\u2010Verlag, New York, 1983, pp. 227\u2013239.","DOI":"10.1007\/BFb0112537"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1137\/0134014"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479896302692"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/050637315","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:45:00Z","timestamp":1787334300000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/050637315"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,1]]},"references-count":24,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2007,1]]}},"alternative-id":["10.1137\/050637315"],"URL":"https:\/\/doi.org\/10.1137\/050637315","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,1]]}}}