{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T21:44:39Z","timestamp":1791150279867,"version":"4.1.0"},"reference-count":32,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[1993,9]]},"abstract":"<jats:p>As with many other linear algebra algorithms, devising a portable implementation of sparse Cholesky factorization that performs well on the broad range of computer architectures currently available is a formidable challenge. Even after limiting the attention to machines with only one processor, as has been done in this paper, there are still several interesting issues to consider. For dense matrices, it is well known that block factorization algorithms are the best means of achieving this goal. This approach is taken for sparse factorization as well.<\/jats:p>\n                  <jats:p>This paper has two primary goals. First, two sparse Cholesky factorization algorithms, the multifrontal method and a blocked left-looking sparse Cholesky method, are examined in a systematic and consistent fashion, both to illustrate the strengths of the blocking techniques in general and to obtain a fair evaluation of the two approaches, Second, the impact of various implementation techniques on time and storage efficiency is assessed, paying particularly close attention to the work-storage requirement of the two methods and their variants.<\/jats:p>","DOI":"10.1137\/0914063","type":"journal-article","created":{"date-parts":[[2005,3,1]],"date-time":"2005-03-01T03:41:55Z","timestamp":1109648515000},"page":"1034-1056","source":"Crossref","is-referenced-by-count":165,"title":["Block Sparse Cholesky Algorithms on Advanced Uniprocessor Computers"],"prefix":"10.1137","volume":"14","author":[{"given":"Esmond G.","family":"Ng","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Barry W.","family":"Peyton","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,13]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1177\/109434208900300303"},{"key":"R2","doi-asserted-by":"crossref","unstructured":"E. 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Sherman,  A comparison of three column-based distributed sparse factorization schemes, Tech. Report , YALEU\/DCS\/RR-810, Department of Computer Science, Yale University, New Haven, CT,  1990","DOI":"10.21236\/ADA228143"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1177\/109434208700100403"},{"key":"R8","unstructured":"E. Chu, A. George, J. W.H. Liu, E. G.Y. Ng,  User's guide for SPARSPAK-A: Waterloo sparse linear equations package, Tech. Report, CS-84-36, University of Waterloo, Waterloo, Ontario, Canada,  1984"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8191(87)90006-8"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1145\/1271.319413"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/1026003"},{"key":"R12","volume-title":"Direct Methods for Sparse Matrices","author":"Duff I.","year":"1987"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1145\/62038.62043"},{"key":"R14","unstructured":"I. Duff, J. Reid,  MA27\u2014A set of Fortran subroutines for solving sparse symmetric sets of linear equations, Tech. Report, AERE R 10533, Harwell, England,  1982"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1145\/356044.356047"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620180804"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1007\/BF01407878"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1137\/0909021"},{"key":"R19","volume-title":"Computer solution of large sparse positive definite systems","author":"George A.","year":"1981"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1137\/0912063"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1145\/6497.6499"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1145\/7921.11325"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1145\/76909.76911"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1137\/1034004"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1145\/103147.103159"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1137\/0914048"},{"key":"R27","unstructured":"E. Rothberg, A. Gupta,  A comparative evaluation of nodal and supernodal parallel sparse matrix factorization: Detailed simulation results, Tech. Report, STAN-CS-90-1305, Stanford University, Stanford, CA,  1990"},{"key":"R28","doi-asserted-by":"crossref","unstructured":"E. Rothberg, A. Gupta,  An evaluation of left-looking right-looking and multifrontal approaches to sparse Cholesky factorization on hierarchical-memory machines, Tech. Report, STAN-CS-91-1377, Stanford University, Stanford, CA,  1991","DOI":"10.21236\/ADA326874"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1145\/114697.116809"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1145\/356004.356006"},{"key":"R31","unstructured":"A. Sherman,  On the efficient solution of sparse systems of linearand nonlinear equations, Tech. Report, 46, Department of Computer Science, Yale University, New Haven, CT,  1975"},{"key":"R32","unstructured":"C. Yang,  A vector\/parallel implementation of the multifrontal method for sparse symmetric definite linear systems on the Cray Y-MP,  1990, Cray Research Inc., Mendota Heights, MN, manuscript"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/0914063","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:33:25Z","timestamp":1787326405000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/0914063"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,9]]},"references-count":32,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1993,9]]}},"alternative-id":["10.1137\/0914063"],"URL":"https:\/\/doi.org\/10.1137\/0914063","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,9]]}}}