{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,26]],"date-time":"2026-09-26T16:57:50Z","timestamp":1790441870339,"version":"4.1.0"},"reference-count":27,"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":[[1998,1]]},"abstract":"<jats:p>The QR factorization with column pivoting (QRP), originally suggested by Golub [Numer. Math., 7 (1965), 206--216], is a popular approach to computing rank-revealing factorizations. Using Level 1 BLAS, it was implemented in LINPACK, and, using Level 2 BLAS, in LAPACK. While the Level 2 BLAS version delivers superior performance in general, it may result in worse performance for large matrix sizes due to cache effects. We introduce a modification of the QRP algorithm which allows the use of Level 3 BLAS kernels while maintaining the numerical behavior of the LINPACK and LAPACK implementations. Experimental comparisons of this approach with the LINPACK and LAPACK implementations on IBM RS\/6000, SGI R8000, and DEC AXP platforms show considerable performance improvements.<\/jats:p>","DOI":"10.1137\/s1064827595296732","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1486-1494","source":"Crossref","is-referenced-by-count":81,"title":["A BLAS-3 Version of the QR Factorization with Column Pivoting"],"prefix":"10.1137","volume":"19","author":[{"given":"Gregorio","family":"Quintana-Ort\u00ed","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaobai","family":"Sun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christian H.","family":"Bischof","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","unstructured":"E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. DuCroz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorensen,\n                      LAPACK User\u2019s Guide Release\n                      2.0, SIAM, Philadelphia, 1994."},{"key":"R2","doi-asserted-by":"crossref","unstructured":"C. H. Bischof,\n                      A block QR factorization algorithm using restricted pivoting\n                      , in Proc. SUPERCOMPUTING \u201989, Baltimore, MD, ACM Press, New York, 1989, pp. 248\u2013256.","DOI":"10.1145\/76263.76290"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/0912002"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/0912073"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/BF02139475"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1109\/78.157185"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(87)90103-0"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479891223781"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1145\/77626.79170"},{"key":"R10","doi-asserted-by":"crossref","unstructured":"J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart,\n                      LINPACK Users\u2019 Guide\n                      , SIAM, Philadelphia, 1979.","DOI":"10.1137\/1.9781611971811"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1145\/42288.42291"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/0907060"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/BF01436075"},{"key":"R14","unstructured":"G. H. Golub and C. F. V. Loan,\n                      Matrix Computations\n                      , 2nd ed., The Johns Hopkins University Press, Baltimore, MD, 1989."},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/0907053"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8396(87)90005-7"},{"key":"R17","unstructured":"T. A. Grandine,\n                      Rank Deficient Interpolation and Optimal Design: An Example\n                      , Tech. Report SCA\u2013TR\u2013113, Engineering and Scientific Services Division, Boeing Computer Services, Seattle, WA, February 1989."},{"key":"R18","unstructured":"M. Gu and S. Eisenstat,\n                      An Efficient Algorithm for Computing a Strong Rank\u2010Revealing Factorization\n                      , Tech. Report YALEU\/DCS\/RR\u2010967, Department of Computer Science, Yale University, New Haven, CT, 1994."},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/0911028"},{"key":"R20","first-page":"213","volume":"58","author":"Hong Y. P.","year":"1992","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1111\/j.2044-8317.1957.tb00179.x"},{"key":"R22","unstructured":"S. F. Hsieh, K. J. R. Liu, and K. Yao,\n                      Comparisons of truncated QR and SVD methods for AR spectral estimations\n                      , in SVD and Signal Processing II, R. J. Vaccaro, ed., Elsevier Science Publishers, New York, 1991, pp. 403\u2013418."},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1145\/355841.355847"},{"key":"R24","doi-asserted-by":"crossref","unstructured":"J. Mor\u00e9,\n                      The Levenberg\u2010Marquardt algorithm: Implementation and theory\n                      , in Proc. Dundee Conference on Numerical Analysis, G. A. Watson, ed., Springer\u2010Verlag, Berlin, 1978.","DOI":"10.1007\/BFb0067700"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022395308695"},{"key":"R26","unstructured":"D. Pierce, Sparse matrix techniques for a sparse rank revealing QR factorization, Mita, Tokyo, 1992, 21\u2013261197995"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1137\/0910005"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827595296732","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:20:59Z","timestamp":1787332859000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827595296732"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,1]]},"references-count":27,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1998,1]]}},"alternative-id":["10.1137\/S1064827595296732"],"URL":"https:\/\/doi.org\/10.1137\/s1064827595296732","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,1]]}}}