{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T07:11:30Z","timestamp":1787382690199,"version":"build-2736575974"},"reference-count":12,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[1993,5]]},"abstract":"<jats:p>This paper presents an algorithm for maintaining Cholesky factors of symmetric positive definite matrices under arbitrary rank-one changes. The algorithm synthesizes Carlson\u2019s up-dating algorithm, and the downdating algorithm recently suggested by Pan to arrive at an algorithm which is both simple and allows for the pipelining of up- and downdates (in any order). On an array of $O(n^2 )$ processors, the algorithm allows an $n \\times n$ matrix to be updated at a cost per update that is independent of n. Implementation results on the 1024-processor AMT DAP-510 emphasize the simplicity and practicality of the proposed scheme.<\/jats:p>","DOI":"10.1137\/0914042","type":"journal-article","created":{"date-parts":[[2005,3,1]],"date-time":"2005-03-01T03:41:55Z","timestamp":1109648515000},"page":"670-676","source":"Crossref","is-referenced-by-count":4,"title":["A Cholesky Up- and Downdating Algorithm for Systolic and SIMD Architectures"],"prefix":"10.1137","volume":"14","author":[{"given":"Christian H.","family":"Bischof","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"C.-T.","family":"Pan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ping Tak Peter","family":"Tang","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":"10.1016\/0024-3795(88)90158-9"},{"key":"R2","unstructured":"C. H. Bischof, C.T. Pan, P. T. P. Tang,  Stable Cholesky up- and downdating algorithms for systolic and SIMD architectures, Tech. Rep., MCS-P167-0790, Mathematics and Computer Science Div., Argonne National Laboratory, Argonne, IL,  1990"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/0908031"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.2514\/3.6907"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1974-0343558-6"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/0912005"},{"key":"R7","volume-title":"Parallel Supercomputing in SIMD Architectures","author":"Hord R. M.","year":"1990"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01933218"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(89)90363-4"},{"key":"R10","unstructured":"M. Saunders,  Large-scale linear programming using the Cholesky factorization, Tech. Rep., STAN-CS-72-252, Dept. of Computer Science, Stanford Univ., Palo Alto, CA,  1972"},{"key":"R11","first-page":"389","volume-title":"VLSI and Modern Signal Processing","author":"Schreiber R.","year":"1985"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1007\/BF01935052"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/0914042","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:28:40Z","timestamp":1787326120000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/0914042"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,5]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1993,5]]}},"alternative-id":["10.1137\/0914042"],"URL":"https:\/\/doi.org\/10.1137\/0914042","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,5]]}}}