{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T15:24:40Z","timestamp":1759332280641,"version":"3.40.3"},"publisher-location":"Cham","reference-count":26,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319321486"},{"type":"electronic","value":"9783319321493"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-319-32149-3_13","type":"book-chapter","created":{"date-parts":[[2016,4,1]],"date-time":"2016-04-01T02:24:42Z","timestamp":1459477482000},"page":"128-137","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["LU Preconditioning for Overdetermined Sparse Least Squares Problems"],"prefix":"10.1007","author":[{"given":"Gary W.","family":"Howell","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marc","family":"Baboulin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,4,2]]},"reference":[{"key":"13_CR1","unstructured":"Amestoy, P.R., Guermouche, A., L\u2019Excellent, J.-Y., Pralet, S.: MUMPS: a MUltifrontal Parallel sparse direct Solver (2014). http:\/\/mumps.enseeiht.fr\/index.php?page=home"},{"issue":"1","key":"13_CR2","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1260\/174830109787186541","volume":"3","author":"M Baboulin","year":"2009","unstructured":"Baboulin, M., Giraud, L., Gratton, S., Langou, J.: Parallel tools for solving incremental dense least squares problems. Application to space geodesy. J. Algorithms Comput. Technol. 3(1), 117\u2013133 (2009)","journal-title":"J. Algorithms Comput. Technol."},{"key":"13_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1007\/978-3-642-55224-3_13","volume-title":"Parallel Processing and Applied Mathematics","author":"M Baboulin","year":"2014","unstructured":"Baboulin, M., Gratton, S., Lacroix, R., Laub, A.J.: Statistical estimates for the conditioning of linear least squares problems. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wa\u015bniewski, J. (eds.) PPAM 2013, Part I. LNCS, vol. 8384, pp. 124\u2013133. Springer, Heidelberg (2014)"},{"key":"13_CR4","unstructured":"Bateman, D., Adler, A.: Sparse matrix implementation in octave (2006). arxiv.org\/pdf\/cs\/0604006.pdf"},{"key":"13_CR5","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1002\/nla.320","volume":"10","author":"M Benzi","year":"2003","unstructured":"Benzi, M., Tuma, M.: A robust incomplete factorization preconditioner for positive definite matrices. Numer. Linear Algebra Appl. 10, 385\u2013400 (2003)","journal-title":"Numer. Linear Algebra Appl."},{"key":"13_CR6","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971484","volume-title":"Numerical Methods for Least Squares Problems","author":"\u00c5 Bj\u00f6rck","year":"1996","unstructured":"Bj\u00f6rck, \u00c5.: Numerical Methods for Least Squares Problems. SIAM, Philadelphia (1996)"},{"key":"13_CR7","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/0024-3795(80)90158-5","volume":"34","author":"A Bj\u00f6rck","year":"1980","unstructured":"Bj\u00f6rck, A., Duff, I.S.: A direct method for the solution of sparse linear least squares problems. Linear Algebra Appl. 34, 43\u201367 (1980)","journal-title":"Linear Algebra Appl."},{"key":"13_CR8","first-page":"26","volume":"8","author":"A Bj\u00f6rck","year":"1999","unstructured":"Bj\u00f6rck, A., Yuan, J.Y.: Preconditioners for least squares problems by \n$$LU$$\n factorization. Electron. Trans. Numer. Anal. 8, 26\u201335 (1999)","journal-title":"Electron. Trans. Numer. Anal."},{"key":"13_CR9","unstructured":"Davis, T.: The University of Florida sparse matrix collection. http:\/\/www.cise.ufl.edu\/research\/sparse\/matrices\/"},{"key":"13_CR10","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718881","volume-title":"Direct Methods for Sparse Linear Systems","author":"T Davis","year":"2006","unstructured":"Davis, T.: Direct Methods for Sparse Linear Systems. SIAM, Philadelphia (2006)"},{"key":"13_CR11","volume-title":"Matrix Computations","author":"GH Golub","year":"1996","unstructured":"Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore (1996)","edition":"3"},{"key":"13_CR12","doi-asserted-by":"publisher","first-page":"529","DOI":"10.1137\/S089547980139604X","volume":"24","author":"A Gupta","year":"2002","unstructured":"Gupta, A.: Improved symbolic and numerical factorization algorithms for unsymmetric sparse matrices. SIAM J. Matrix Anal. Appl. 24, 529\u2013552 (2002)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"13_CR13","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1137\/0905023","volume":"5","author":"WW Hager","year":"1984","unstructured":"Hager, W.W.: Condition estimates. SIAM J. Sci. Stat. Comput. 5, 311\u2013316 (1984)","journal-title":"SIAM J. Sci. Stat. Comput."},{"issue":"4","key":"13_CR14","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1137\/0905037","volume":"5","author":"MT Heath","year":"1984","unstructured":"Heath, M.T.: Numerical methods for large sparse linear squares problems. SIAM J. Sci. Stat. Comput. 5(4), 497\u2013513 (1984)","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"13_CR15","doi-asserted-by":"publisher","first-page":"1185","DOI":"10.1137\/S0895479899356080","volume":"21","author":"NJ Higham","year":"2000","unstructured":"Higham, N.J., Tisseur, F.: A block algorithm for matrix 1-norm estimation with an application to 1-norm pseudospectra. SIAM J. Matrix Anal. Appl. 21, 1185\u20131201 (2000)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"13_CR16","unstructured":"Howell, G., Baboulin, M.: Data and plots for lsqr, lsqrLU and lsqrLUQR (2015). http:\/\/ncsu.edu\/hpc\/Documets\/Publications\/gary_howell\/contents.html"},{"issue":"4","key":"13_CR17","doi-asserted-by":"publisher","first-page":"978","DOI":"10.1137\/0905067","volume":"5","author":"A Jennings","year":"1984","unstructured":"Jennings, A., Ajiz, M.A.: Incomplete methods for solving \n$$A^TAx = b$$\n. SIAM J. Sci. Stat. Comput. 5(4), 978\u2013987 (1984)","journal-title":"SIAM J. Sci. Stat. Comput."},{"issue":"2","key":"13_CR18","doi-asserted-by":"publisher","first-page":"524","DOI":"10.1137\/050633032","volume":"28","author":"N Li","year":"2006","unstructured":"Li, N., Saad, Y.: MIQR: a multilevel incomplete \n$$QR$$\n preconditioner for large sparse least-squares problems. SIAM J. Matrix Anal. Appl. 28(2), 524\u2013550 (2006)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"3","key":"13_CR19","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1145\/1089014.1089017","volume":"31","author":"XS Li","year":"2005","unstructured":"Li, X.S.: An overview of SuperLU: algorithms, implementation, and user interface. ACM Trans. Math. Softw. 31(3), 302\u2013325 (2005)","journal-title":"ACM Trans. Math. Softw."},{"issue":"9","key":"13_CR20","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1145\/779359.779361","volume":"29","author":"XS Li","year":"2003","unstructured":"Li, X.S., Demmel, J.W.: SuperLU\n$$\\_$$\nDIST: a scalable distributed-memory sparse direct solver for unsymmetric linear systems. ACM Trans. Math. Softw. 29(9), 110\u2013140 (2003)","journal-title":"ACM Trans. Math. Softw."},{"key":"13_CR21","first-page":"43","volume":"2","author":"M Lourakis","year":"2010","unstructured":"Lourakis, M.: Sparse non-linear least squares optimization for geometric vision. Eur. Conf. Comput. Vis. 2, 43\u201356 (2010)","journal-title":"Eur. Conf. Comput. Vis."},{"key":"13_CR22","doi-asserted-by":"publisher","DOI":"10.1007\/b98874","volume-title":"Numerical Optimization","author":"J Nocedal","year":"1999","unstructured":"Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (1999)"},{"issue":"1","key":"13_CR23","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1145\/355984.355989","volume":"8","author":"C Paige","year":"1982","unstructured":"Paige, C., Saunders, M.: An algorithm for sparse linear equations and sparse least squares. ACM Trans. Math. Softw. 8(1), 43\u201371 (1982)","journal-title":"ACM Trans. Math. Softw."},{"key":"13_CR24","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1093\/comjnl\/13.3.309","volume":"13","author":"G Peters","year":"1970","unstructured":"Peters, G., Wilkinson, J.H.: The least squares problem and pseudo-inverses. Comput. J. 13, 309\u2013316 (1970)","journal-title":"Comput. J."},{"key":"13_CR25","volume-title":"Iterative Methods for Sparse Linear Systems","author":"Y Saad","year":"2000","unstructured":"Saad, Y.: Iterative Methods for Sparse Linear Systems, 2nd edn. SIAM, Philadelphia (2000)","edition":"2"},{"key":"13_CR26","unstructured":"Schenk, O., G\u00e4rtner, K.: PARDISO User Guide (2014). http:\/\/www.pardiso-project.org\/manual\/manual.pdf"}],"container-title":["Lecture Notes in Computer Science","Parallel Processing and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-32149-3_13","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,15]],"date-time":"2020-12-15T01:09:20Z","timestamp":1607994560000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-32149-3_13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783319321486","9783319321493"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-32149-3_13","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2016]]},"assertion":[{"value":"2 April 2016","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}