{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:33:39Z","timestamp":1787337219260,"version":"build-2736575974"},"reference-count":66,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>Three techniques for improving the robustness and performance of incomplete factorization preconditioners for sparse systems with symmetric positive definite or mildly indefinite coefficient matrices are introduced. The primary contribution is two new block algorithms for incomplete factorization that result in an improvement in the performance of both the preconditioner generation and the iterative solution phases. One of the algorithms applies to matrices that have a natural block structure in their original form, and the other applies to matrices without natural dense blocks. Additionally, two relatively simple but highly effective heuristic strategies are introduced. These include selecting the solver based on the definiteness properties of the preconditioner and automatic selection and tuning of incomplete factorization parameters. All three techniques have adaptive components; i.e., the preconditioner-solver combination chooses parameters or algorithmic components based on the properties of the coefficient matrix and its incomplete factors. Two of the three techniques are applicable to incomplete LU factorization for unsymmetric systems as well.<\/jats:p>","DOI":"10.1137\/080727695","type":"journal-article","created":{"date-parts":[[2010,2,5]],"date-time":"2010-02-05T18:13:52Z","timestamp":1265393632000},"page":"84-110","source":"Crossref","is-referenced-by-count":25,"title":["Adaptive Techniques for Improving the Performance of Incomplete Factorization Preconditioning"],"prefix":"10.1137","volume":"32","author":[{"given":"Anshul","family":"Gupta","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thomas","family":"George","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,2,5]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620200511"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/0916081"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1145\/76909.76910"},{"key":"R4","unstructured":"H. Avron, A. Gupta, and S. Toledo,\n                      New Krylov-Subspace Solvers for Hermitian Positive Definite Matrices with Indefinite Preconditioners\n                      , Technical Report RC 24698, IBM T. J. Watson Research Center, Yorktown Heights, NY, 2008."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(86)90121-7"},{"key":"R6","unstructured":"S. Balay, K. Buschelman, V. Eijkhout, W. D. Gropp, D. Kaushik, M. G. Knepley, L. Curfman McInnes, B. F. Smith, and H. Zhang,\n                      PETSc Users Manual\n                      , Technical Report ANL-95\/11 - Revision 2.3.3, Argonne National Laboratory, Argonne, IL, 2007."},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/0724070"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2002.7176"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(01)00235-3"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1002\/nla.320"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827502403411"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/040608374"},{"key":"R13","unstructured":"M. Bollh\u00f6fer, Y. Saad, and O. Schenk,\n                      ILUPACK\u2014Preconditioning Software Package\n                      , available online at http:\/\/www.math.tu-berlin.de\/ilupack (2008)."},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/S106482759833913X"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1177\/109434200101500106"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1145\/290200.287639"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595281575"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(97)00171-4"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827594270415"},{"key":"R20","doi-asserted-by":"crossref","unstructured":"E. Cuthill and J. McKee,\n                      Reducing the bandwidth of sparse symmetric matrices\n                      , in Proceedings of the 24th National Conference of the ACM, ACM Press, New York, 1969,pp. 152\u2013172.","DOI":"10.1145\/800195.805928"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1080\/00207169208804110"},{"key":"R22","unstructured":"T. A. Davis,\n                      The University of Florida Sparse Matrix Collection\n                      , Technical report, Department of Computer Science, University of Florida, Tallahassee, FL, 2007."},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1007\/s101070100263"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1145\/77626.79170"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1145\/42288.42291"},{"key":"R26","doi-asserted-by":"crossref","unstructured":"I. S. Duff,\n                      Sparse numerical linear algebra: Direct methods and preconditioning\n                      , in The State of the Art in Numerical Analysis, I. S. Duff and G. A. Watson, eds., Oxford University Press, Oxford, 1997, pp. 27\u201362. Also available as Technical report RAL-TR-96-047, Rutherford Appleton Laboratory, Oxfordshire, UK.","DOI":"10.1093\/oso\/9780198500148.003.0002"},{"key":"R27","unstructured":"I. S. Duff, A. M. Erisman, and J. K. Reid,\n                      Direct Methods for Sparse Matrices\n                      , Oxford University Press, Oxford, UK, 1990."},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1007\/BF01932738"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1145\/356044.356047"},{"key":"R30","doi-asserted-by":"crossref","unstructured":"R. D. Falgout and U. M. Yang,\n                      Hypre: A Library of High Performance Preconditioners,\n                      Technical report UCRL-JC-146175, Lawrence Livermore National Laboratory, Livermore, CA, 2001. Paper also appears in Proceedings of the International Conference on Computational Science, Part III, Lecture Notes in Comput. Sci. 2329, P. M. A. Sloot et al., eds., Springer, Berlin, 2002, pp. 632\u2013641.","DOI":"10.1007\/3-540-47789-6_66"},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1137\/0917009"},{"key":"R32","doi-asserted-by":"publisher","DOI":"10.1145\/225545.225551"},{"key":"R33","unstructured":"M. W. Gee, C. M. Siefert, J. J. Hu, R. S. Tuminaro, and M. G. Sala,\n                      ML $5.0$ Smoothed Aggregation User's Guide\n                      , Technical Report SAND2006-2649, Sandia National Laboratories, Livermore, CA, 2006."},{"key":"R34","unstructured":"A. George and J. W.H. Liu,\n                      Computer Solution of Large Sparse Positive Definite Systems\n                      , Prentice-Hall, Englewood Cliffs, NJ, 1981."},{"key":"R35","unstructured":"T. George, A. Gupta, and V. Sarin,\n                      An experimental evaluation of iterative solvers for large SPD systems of linear equations\n                      , in Proceedings of the 10th Copper Mountain Conference on Iterative Methods, April 2008. Available online at http:\/\/www.cs.umn.edu\/ $\\!_{^{\\sim}}\\!$agupta\/doc\/copper08.pdf."},{"key":"R36","unstructured":"T. George, A. Gupta, and V. Sarin,\n                      An Empirical Analysis of Iterative Solver Performance for SPD Systems\n                      , Technical Report RC 24737, IBM T. J. Watson Research Center, Yorktown Heights, NY, 2009. A short version submitted to ACM Trans. Math. Software."},{"key":"R37","doi-asserted-by":"crossref","unstructured":"T. George, A. Gupta, and V. Sarin,\n                      A Recommendation System for Preconditioned Iterative solvers\n                      , Technical Report RC 24600, IBM T. J. Watson Research Center, Yorktown Heights, NY, 2008. A short version appears in Proceedings of the IEEE International Conference on Data Mining (Pisa, Italy), 2008, pp. 803\u2013808.","DOI":"10.1109\/ICDM.2008.105"},{"key":"R38","first-page":"409","volume":"24","author":"Gilbert J. R.","year":"2000","journal-title":"Informatica","ISSN":"https:\/\/id.crossref.org\/issn\/0350-5596","issn-type":"print"},{"key":"R39","unstructured":"G. H. Golub and C. Van Loan,\n                      Matrix Computations\n                      , The Johns Hopkins University Press, Baltimore, MD, 1996."},{"key":"R40","doi-asserted-by":"publisher","DOI":"10.1147\/rd.411.0171"},{"key":"R41","unstructured":"A. Gupta,\n                      WSMP: Watson Sparse Matrix Package (Part\n                      I:\n                      Direct Solution of Symmetric Sparse Systems)\n                      , Technical Report RC 21886, IBM T. J. Watson Research Center, Yorktown Heights, NY, 2000. Available online at http:\/\/www.cs.umn.edu\/$\\!_{^{\\sim}}\\!$agupta\/wsmp."},{"key":"R42","unstructured":"A. Gupta,\n                      WSMP: Watson Sparse Matrix Package (Part\n                      III:\n                      Iterative Solution of Sparse Systems),\n                      Technical Report RC 24398, IBM T. J. Watson Research Center, Yorktown Heights, NY, 2007. Available online at http:\/\/www.cs.umn.edu\/$\\!_{^{\\sim}}\\!$agupta\/wsmp."},{"key":"R43","doi-asserted-by":"publisher","DOI":"10.1016\/j.parco.2007.12.003"},{"key":"R44","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(01)00115-5"},{"key":"R45","doi-asserted-by":"publisher","DOI":"10.1145\/1089014.1089021"},{"key":"R46","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827500376193"},{"key":"R47","unstructured":"M. T. Jones and P. E. Plassmann,\n                      Blocksolve95 Users Manual: Scalable Library Software for the Parallel Solution of Sparse Linear Systems\n                      , Technical Report ANL-95\/48, Argonne National Laboratory, Argonne, IL, 1995."},{"key":"R48","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(91)90398-G"},{"key":"R49","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(78)90098-0"},{"key":"R50","doi-asserted-by":"publisher","DOI":"10.1145\/6497.6499"},{"key":"R51","doi-asserted-by":"publisher","DOI":"10.1137\/0611010"},{"key":"R52","doi-asserted-by":"publisher","DOI":"10.1137\/1034004"},{"key":"R53","doi-asserted-by":"publisher","DOI":"10.1137\/0614019"},{"key":"R54","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1980-0559197-0"},{"key":"R55","doi-asserted-by":"publisher","DOI":"10.1145\/355887.355893"},{"key":"R56","unstructured":"E. G.Y. Ng, B. W. Peyton, and P. Raghavan,\n                      A blocked incomplete Cholesky preconditioner for hierarchical-memory computers\n                      , in Iterative Methods in Scientific Computation IV, IMACS Ser. Comput. Appl. Math., D. R. Kincaid and A. C. Elster, eds., Elsevier, Amsterdam, 1999, pp. 211\u2013221."},{"key":"R57","doi-asserted-by":"publisher","DOI":"10.1137\/0712047"},{"key":"R58","doi-asserted-by":"crossref","unstructured":"J. W. Ruge and K. St\u00fcben, in\n                      Multigrid Methods\n                      , Frontiers Appl. Math. 3, S. F. McCormick, ed., SIAM, Philadelphia, 1987, pp. 73\u2013130.","DOI":"10.1137\/1.9781611971057.ch4"},{"key":"R59","doi-asserted-by":"publisher","DOI":"10.1002\/nla.1680010405"},{"key":"R60","doi-asserted-by":"crossref","unstructured":"Y. Saad,\n                      Iterative Methods for Sparse Linear Systems\n                      , 2nd ed., SIAM, Philadelphia, 2003.","DOI":"10.1137\/1.9780898718003"},{"key":"R61","doi-asserted-by":"publisher","DOI":"10.1137\/0907058"},{"key":"R62","doi-asserted-by":"publisher","DOI":"10.1137\/S106482759732753X"},{"key":"R63","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(91)90383-8"},{"key":"R64","doi-asserted-by":"crossref","unstructured":"R. S. Tuminaro,\n                      Parallel smoothed aggregation multigrid: Aggregation strategies on massively parallel machines\n                      , in Proceedings of the 2000 ACM\/IEEE Conference on Supercomputing (Supercomputing '00), CDROM, 2000.","DOI":"10.1109\/SC.2000.10008"},{"key":"R65","doi-asserted-by":"publisher","DOI":"10.2118\/8252-PA"},{"key":"R66","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1954-0059635-7"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080727695","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:50:19Z","timestamp":1787334619000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080727695"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":66,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/080727695"],"URL":"https:\/\/doi.org\/10.1137\/080727695","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}