{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,18]],"date-time":"2026-04-18T06:50:42Z","timestamp":1776495042524,"version":"3.51.2"},"reference-count":49,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2008,7,1]],"date-time":"2008-07-01T00:00:00Z","timestamp":1214870400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[2008,7,15]]},"abstract":"<jats:p>By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many sparse linear algebra algorithms can be significantly enhanced while maintaining the 64-bit accuracy of the resulting solution. These ideas can be applied to sparse multifrontal and supernodal direct techniques and sparse iterative techniques such as Krylov subspace methods. The approach presented here can apply not only to conventional processors but also to exotic technologies such as Field Programmable Gate Arrays (FPGA), Graphical Processing Units (GPU), and the Cell BE processor.<\/jats:p>","DOI":"10.1145\/1377596.1377597","type":"journal-article","created":{"date-parts":[[2008,7,22]],"date-time":"2008-07-22T13:04:05Z","timestamp":1216731845000},"page":"1-22","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":68,"title":["Using Mixed Precision for Sparse Matrix Computations to Enhance the Performance while Achieving 64-bit Accuracy"],"prefix":"10.1145","volume":"34","author":[{"given":"Alfredo","family":"Buttari","sequence":"first","affiliation":[{"name":"ENS Lyon"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jack","family":"Dongarra","sequence":"additional","affiliation":[{"name":"University of Tennessee Knoxville and Oak Ridge National Laboratory and University of Manchester"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jakub","family":"Kurzak","sequence":"additional","affiliation":[{"name":"University of Tennessee Knoxville"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Piotr","family":"Luszczek","sequence":"additional","affiliation":[{"name":"The MathWorks"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stanimir","family":"Tomov","sequence":"additional","affiliation":[{"name":"University of Tennessee Knoxville"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2008,7]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(99)00242-X"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479899358194"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.parco.2005.07.004"},{"key":"e_1_2_1_4_1","doi-asserted-by":"crossref","unstructured":"Anderson E. Bai Z. Bischof C. Blackford S. L. Demmel J. W. Dongarra J. J. Croz J. D. Greenbaum A. Hammarling S. McKenney A. and Sorensen D. C. 1999. LAPACK User's Guide 3rd Ed. Society for Industrial and Applied Mathematics Philadelphia PA. Anderson E. Bai Z. Bischof C. Blackford S. L. Demmel J. W. Dongarra J. J. Croz J. D. Greenbaum A. Hammarling S. McKenney A. and Sorensen D. C. 1999. LAPACK User's Guide 3rd Ed. Society for Industrial and Applied Mathematics Philadelphia PA.","DOI":"10.1137\/1.9780898719604"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1177\/109434208700100403"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1137\/0612048"},{"key":"e_1_2_1_7_1","unstructured":"Balay S. Buschelman K. Gropp W. D. Kaushik D. Knepley M. G. McInnes L. C. Smith B. F. and Zhang H. 2001. PETSc Web page. http:\/\/www.mcs.anl.gov\/petsc. Balay S. Buschelman K. Gropp W. D. Kaushik D. Knepley M. G. McInnes L. C. Smith B. F. and Zhang H. 2001. PETSc Web page. http:\/\/www.mcs.anl.gov\/petsc."},{"key":"e_1_2_1_8_1","volume-title":"Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods","author":"Barrett R.","unstructured":"Barrett , R. , Berry , M. , Chan , T. F. , Demmel , J. , Donato , J. M. , Dongarra , J. , Eijkhout , V. , Pozo , R. , Romine , C. , and der Vorst , H. V. 1994. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods . Society for Industrial and Applied Mathematics , Philadelphia, PA . http:\/\/www.netlib.org\/templates\/Templates.html. Barrett, R., Berry, M., Chan, T. F., Demmel, J., Donato, J. M., Dongarra, J., Eijkhout, V., Pozo, R., Romine, C., and der Vorst, H. V. 1994. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. Society for Industrial and Applied Mathematics, Philadelphia, PA. http:\/\/www.netlib.org\/templates\/Templates.html."},{"key":"e_1_2_1_9_1","volume-title":"Oxford","author":"Bj\u00f6rck A.","unstructured":"Bj\u00f6rck , A. 1990. Iterative refinement and reliable computing . In Reliable Numerical Computation, M. G. Cox and S. Hammarling, Eds. Oxford University Press , Oxford, UK , 249--266. Bj\u00f6rck, A. 1990. Iterative refinement and reliable computing. In Reliable Numerical Computation, M. G. Cox and S. Hammarling, Eds. Oxford University Press, Oxford, UK, 249--266."},{"key":"e_1_2_1_10_1","unstructured":"Buttari A. Dongarra J. Kurzak J. Luszczek P. and Tomov S. 2006. Computations to enhance the performance while achieving the 64-bit accuracy. Tech. rep. UT-CS-06-584 University of Tennessee Knoxville. LAPACK Working Note 180. Buttari A. Dongarra J. Kurzak J. Luszczek P. and Tomov S. 2006. Computations to enhance the performance while achieving the 64-bit accuracy. Tech. rep. UT-CS-06-584 University of Tennessee Knoxville. LAPACK Working Note 180."},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/305658.287640"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/992200.992205"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2004.840848"},{"key":"e_1_2_1_14_1","volume-title":"Applied Numerical Linear Algebra","author":"Demmel J. W.","unstructured":"Demmel , J. W. 1997. Applied Numerical Linear Algebra . Society for Industrial and Applied Mathematics , Philadelphia, PA . Demmel, J. W. 1997. Applied Numerical Linear Algebra. Society for Industrial and Applied Mathematics, Philadelphia, PA."},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479895291765"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479897317685"},{"key":"e_1_2_1_17_1","unstructured":"Dongarra J. J. and Eijkhout V. 2002. Self-adapting numerical software for next generation applications. Tech. rep. ICL-UT-02-07 Innovative Computing Lab University of Tennessee Lapack Working Note 157. http:\/\/icl.cs.utk.edu\/iclprojects\/pages\/sans.html. Dongarra J. J. and Eijkhout V. 2002. Self-adapting numerical software for next generation applications. Tech. rep. ICL-UT-02-07 Innovative Computing Lab University of Tennessee Lapack Working Note 157. http:\/\/icl.cs.utk.edu\/iclprojects\/pages\/sans.html."},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/356044.356047"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479894246905"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1137\/S003614450139961"},{"key":"e_1_2_1_21_1","unstructured":"Forsythe G. E. and Moler C. B. 1967. Computer Solution of Linear Algebraic Systems. Prentice-Hall Englewood Cliffs NJ. Forsythe G. E. and Moler C. B. 1967. Computer Solution of Linear Algebraic Systems . Prentice-Hall Englewood Cliffs NJ."},{"key":"e_1_2_1_22_1","volume-title":"Simulationstechnique 18th Symposium in Erlangen. F. H\u00fclsemann, M. Kowarschik, and U. R\u00fcde, Eds.","volume":"144","author":"G\u00f6ddeke D.","unstructured":"G\u00f6ddeke , D. , Strzodka , R. , and Turek , S . 2005. Accelerating double precision FEM simulations with GPUs . In Simulationstechnique 18th Symposium in Erlangen. F. H\u00fclsemann, M. Kowarschik, and U. R\u00fcde, Eds. Vol. Frontiers in Simulation. SCS Publishing House e.V., 139-- 144 . G\u00f6ddeke, D., Strzodka, R., and Turek, S. 2005. Accelerating double precision FEM simulations with GPUs. In Simulationstechnique 18th Symposium in Erlangen. F. H\u00fclsemann, M. Kowarschik, and U. R\u00fcde, Eds. Vol. Frontiers in Simulation. SCS Publishing House e.V., 139--144."},{"key":"e_1_2_1_23_1","unstructured":"Golub G. H. and Loan C. F. V. 1989. Matrix Computations 2nd Ed. Johns Hopkins University Press Baltimore MD. Golub G. H. and Loan C. F. V. 1989. Matrix Computations 2nd Ed. Johns Hopkins University Press Baltimore MD."},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827597323415"},{"key":"e_1_2_1_25_1","unstructured":"Gropp W. D. Kaushik D. K. Keyes D. E. and Smith B. F. 2000. Latency bandwidth and concurrent issue limitations in high-performance CFD. Tech. rep. ANL\/MCS-P850-1000 Argonne National Laboratory. Gropp W. D. Kaushik D. K. Keyes D. E. and Smith B. F. 2000. Latency bandwidth and concurrent issue limitations in high-performance CFD. Tech. rep. ANL\/MCS-P850-1000 Argonne National Laboratory."},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8191(00)00075-2"},{"key":"e_1_2_1_27_1","volume-title":"An Introduction to Continuum Mechanics","author":"Gurtin M. E.","unstructured":"Gurtin , M. E. 1981. An Introduction to Continuum Mechanics . Academic Press , New York, NY . Gurtin, M. E. 1981. An Introduction to Continuum Mechanics. Academic Press, New York, NY."},{"key":"e_1_2_1_28_1","series-title":"Springer Series in Computational Mathematics","volume-title":"Multigrid Methods and Applications","author":"Hackbusch W.","unstructured":"Hackbusch , W. 1985. Multigrid Methods and Applications . Springer Series in Computational Mathematics , Vol. 4 , Springer-Verlag , Berlin, Germany . Hackbusch, W. 1985. Multigrid Methods and Applications. Springer Series in Computational Mathematics, Vol. 4, Springer-Verlag, Berlin, Germany."},{"key":"e_1_2_1_29_1","volume-title":"Accuracy and Stability of Numerical Algorithms","author":"Higham N. J.","unstructured":"Higham , N. J. 2002. Accuracy and Stability of Numerical Algorithms 2 nd Ed. Society for Industrial and Applied Mathematics , Philadelphia, PA . Higham, N. J. 2002. Accuracy and Stability of Numerical Algorithms 2nd Ed. Society for Industrial and Applied Mathematics, Philadelphia, PA.","edition":"2"},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/1188455.1188573"},{"key":"e_1_2_1_32_1","doi-asserted-by":"publisher","DOI":"10.1145\/779359.779361"},{"key":"e_1_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/321386.321394"},{"key":"e_1_2_1_34_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827599362314"},{"key":"e_1_2_1_35_1","doi-asserted-by":"crossref","unstructured":"Quarteroni A. and Valli A. 1999. Domain Decomposition Methods for Partial Differential Equations. Oxford University Press Cambridge UK. Quarteroni A. and Valli A. 1999. Domain Decomposition Methods for Partial Differential Equations . Oxford University Press Cambridge UK.","DOI":"10.1007\/978-94-011-4647-0_11"},{"key":"e_1_2_1_36_1","volume-title":"Department of Computer Science and Engineering","author":"Saad Y.","unstructured":"Saad , Y. 1991. A flexible inner-outer preconditioned GMRES algorithm. Tech. rep. 91-279 , Department of Computer Science and Engineering , University of Minnesota , Minneapolis, MN . Saad, Y. 1991. A flexible inner-outer preconditioned GMRES algorithm. Tech. rep. 91-279, Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN."},{"key":"e_1_2_1_37_1","volume-title":"Iterative Methods for Sparse Linear Systems","author":"Saad Y.","unstructured":"Saad , Y. 2003. Iterative Methods for Sparse Linear Systems . Society for Industrial and Applied Mathematics, Philadelphia , PA. Saad, Y. 2003. Iterative Methods for Sparse Linear Systems. Society for Industrial and Applied Mathematics, Philadelphia, PA."},{"key":"e_1_2_1_38_1","doi-asserted-by":"publisher","DOI":"10.1137\/0907058"},{"key":"e_1_2_1_39_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1506(199607\/08)3:4<329::AID-NLA86>3.0.CO;2-8"},{"key":"e_1_2_1_40_1","unstructured":"Simoncini V. and Szyld D. 2002a. Theory of inexact Krylov subspace methods and applications to scientific computing. Tech. rep. 02-4-12 Department of Mathematics Temple University. Simoncini V. and Szyld D. 2002a. Theory of inexact Krylov subspace methods and applications to scientific computing. Tech. rep. 02-4-12 Department of Mathematics Temple University."},{"key":"e_1_2_1_41_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142902401074"},{"key":"e_1_2_1_42_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-005-0603-8"},{"key":"e_1_2_1_43_1","volume-title":"Matrix algorithms","author":"Stewart G. W.","unstructured":"Stewart , G. W. 2001. Matrix algorithms . Society for Industrial and Applied Mathematics, Philadelphia , PA. Stewart, G. W. 2001. Matrix algorithms. Society for Industrial and Applied Mathematics, Philadelphia, PA."},{"key":"e_1_2_1_44_1","volume-title":"EDGE'06","author":"Strzodka R.","unstructured":"Strzodka , R. and G\u00f6ddeke , D . 2006a. Mixed precision methods for convergent iterative schemes . EDGE'06 , 23.-24. Chapel Hill, NC. Strzodka, R. and G\u00f6ddeke, D. 2006a. Mixed precision methods for convergent iterative schemes. EDGE'06, 23.-24. Chapel Hill, NC."},{"key":"e_1_2_1_45_1","doi-asserted-by":"publisher","DOI":"10.1109\/FCCM.2006.57"},{"key":"e_1_2_1_46_1","doi-asserted-by":"publisher","DOI":"10.1137\/0913048"},{"key":"e_1_2_1_47_1","volume-title":"Relaxation strategies for nested Krylov methods. Technical report TR\/PA\/03\/27","author":"van den Eshof J.","unstructured":"van den Eshof , J. , Sleijpen , G. L. G. , and van Gijzen , M. B. 2003. Relaxation strategies for nested Krylov methods. Technical report TR\/PA\/03\/27 , CERFACS , Toulouse, France . van den Eshof, J., Sleijpen, G. L. G., and van Gijzen, M. B. 2003. Relaxation strategies for nested Krylov methods. Technical report TR\/PA\/03\/27, CERFACS, Toulouse, France."},{"key":"e_1_2_1_48_1","doi-asserted-by":"publisher","DOI":"10.1002\/nla.1680010404"},{"key":"e_1_2_1_49_1","doi-asserted-by":"publisher","DOI":"10.1016\/0377-0427(94)00067-B"},{"key":"e_1_2_1_50_1","volume-title":"The Algebraic Eigenvalue Problem","author":"Wilkinson J. H.","unstructured":"Wilkinson , J. H. 1965. The Algebraic Eigenvalue Problem . Oxford University Press , Oxford, UK . Wilkinson, J. H. 1965. The Algebraic Eigenvalue Problem. Oxford University Press, Oxford, UK."}],"container-title":["ACM Transactions on Mathematical Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1377596.1377597","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1377596.1377597","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T13:57:56Z","timestamp":1750255076000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1377596.1377597"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,7]]},"references-count":49,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,7,15]]}},"alternative-id":["10.1145\/1377596.1377597"],"URL":"https:\/\/doi.org\/10.1145\/1377596.1377597","relation":{},"ISSN":["0098-3500","1557-7295"],"issn-type":[{"value":"0098-3500","type":"print"},{"value":"1557-7295","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,7]]},"assertion":[{"value":"2006-11-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2007-07-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2008-07-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}