{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:33:55Z","timestamp":1787337235716,"version":"build-2736575974"},"reference-count":8,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2001,1]]},"abstract":"<jats:p>The CGNR algorithm is a robust algorithm solving large nonsymmetric linear systems. In this short note, we show that the norm of the error vector of CGNR approximation decreases monotonically during its iteration. Few iterative algorithms have this error reducing property. The result indicates that the simple CGNR algorithm is still a potential one in practical use.<\/jats:p>","DOI":"10.1137\/s1064827500375990","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"2109-2112","source":"Crossref","is-referenced-by-count":3,"title":["CGNR Is an Error Reducing Algorithm"],"prefix":"10.1137","volume":"22","author":[{"given":"Chunguang","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","volume-title":"A survey of preconditioned iterative methods","author":"Bruaset Are","year":"1995"},{"key":"R2","unstructured":"R. Ehrig and P. Deuflhard,\n                      GMERR\u2014An Error Minimizing Variant of GMRES\n                      , Technical report, Konrad\u2010Zuse\u2010Zentrum f\u00fcr Informationstechnik Berlin, Berlin, 1997, http:\/\/www.zib.de\/."},{"key":"R3","unstructured":"C. Li,\n                      Some Researches on the Iterative Methods for Solving Large Sparse Linear Systems\n                      , Ph.D. thesis, Xi\u2019an Jiaotong University, Xi\u2019an, Shaanxi province, People\u2019s Republic of China, 1999."},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/0613049"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(88)90345-7"},{"key":"R6","unstructured":"J. Varah, A survey of iterative methods for sparse linear systems, Proceedings of the fifteenth Manitoba conference on numerical mathematics and computing (Winnipeg, Man., 1985), Vol. 51, 1986, 83\u20139288h:65080"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(91)90397-F"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/0915034"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827500375990","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:51:34Z","timestamp":1787334694000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827500375990"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,1]]},"references-count":8,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2001,1]]}},"alternative-id":["10.1137\/S1064827500375990"],"URL":"https:\/\/doi.org\/10.1137\/s1064827500375990","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,1]]}}}