{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T18:47:12Z","timestamp":1784054832332,"version":"3.55.0"},"reference-count":10,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2005,9,1]],"date-time":"2005-09-01T00:00:00Z","timestamp":1125532800000},"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":[[2005,9]]},"abstract":"<jats:p>The Scalable Library for Eigenvalue Problem Computations (SLEPc) is a software library for computing a few eigenvalues and associated eigenvectors of a large sparse matrix or matrix pencil. It has been developed on top of PETSc and enforces the same programming paradigm.The emphasis of the software is on methods and techniques appropriate for problems in which the associated matrices are sparse, for example, those arising after the discretization of partial differential equations. Therefore, most of the methods offered by the library are projection methods such as Arnoldi or Lanczos, or other methods with similar properties. SLEPc provides basic methods as well as more sophisticated algorithms. It also provides built-in support for spectral transformations such as the shift-and-invert technique. SLEPc is a general library in the sense that it covers standard and generalized eigenvalue problems, both Hermitian and non-Hermitian, with either real or complex arithmetic.SLEPc can be easily applied to real world problems. To illustrate this, several case studies arising from real applications are presented and solved with SLEPc with little programming effort. The addressed problems include a matrix-free standard problem, a complex generalized problem, and a singular value decomposition. The implemented codes exhibit good properties regarding flexibility as well as parallel performance.<\/jats:p>","DOI":"10.1145\/1089014.1089019","type":"journal-article","created":{"date-parts":[[2005,11,7]],"date-time":"2005-11-07T16:00:45Z","timestamp":1131379245000},"page":"351-362","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":884,"title":["SLEPc"],"prefix":"10.1145","volume":"31","author":[{"given":"Vicente","family":"Hernandez","sequence":"first","affiliation":[{"name":"Universidad Polit\u00e9cnica de Valencia, Valencia, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jose E.","family":"Roman","sequence":"additional","affiliation":[{"name":"Universidad Polit\u00e9cnica de Valencia, Valencia, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vicente","family":"Vidal","sequence":"additional","affiliation":[{"name":"Universidad Polit\u00e9cnica de Valencia, Valencia, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2005,9]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"2000. Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide","author":"Bai Z.","unstructured":"Bai , Z. , Demmel , J. , Dongarra , J. , Ruhe , A. , and van der Vorst , H. , Eds. 2000. Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide . SIAM Press , Philadelphia, PA . Available online at http:\/\/www.netlib.org\/etemplates. Bai, Z., Demmel, J., Dongarra, J., Ruhe, A., and van der Vorst, H., Eds. 2000. Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide. SIAM Press, Philadelphia, PA. Available online at http:\/\/www.netlib.org\/etemplates."},{"issue":"2","key":"e_1_2_1_2_1","first-page":"1","article-title":"PETSc users manual. Tech. rep. ANL-95\/11","volume":"2","author":"Balay S.","year":"2004","unstructured":"Balay , S. , Buschelman , K. , Gropp , W. , Kaushik , D. , Knepley , M. , McInnes , L. C. , Smith , B. , and Zhang , H. 2004 . PETSc users manual. Tech. rep. ANL-95\/11 , Rev. 2 . 2 . 1 . Argonne National Laboratory, Argonne, IL. Balay, S., Buschelman, K., Gropp, W., Kaushik, D., Knepley, M., McInnes, L. C., Smith, B., and Zhang, H. 2004. PETSc users manual. Tech. rep. ANL-95\/11, Rev. 2.2.1. Argonne National Laboratory, Argonne, IL.","journal-title":"Rev."},{"key":"e_1_2_1_3_1","unstructured":"Berry M. W. and Browne M. 1999. Understanding Search Engines: Mathematical Modeling and Text Retrieval. SIAM Press Philadelphia PA.   Berry M. W. and Browne M. 1999. Understanding Search Engines: Mathematical Modeling and Text Retrieval. SIAM Press Philadelphia PA."},{"key":"e_1_2_1_4_1","unstructured":"Hernandez V. Roman J. E. and Vidal V. 2004. SLEPc users manual. Tech. rep. DSIC-II\/24\/02---Rev. 2.2.1. D. Sist. Inform. y Comp. Universidad Polit\u00e9cnica de Valencia Valencia Spain.  Hernandez V. Roman J. E. and Vidal V. 2004. SLEPc users manual. Tech. rep. DSIC-II\/24\/02---Rev. 2.2.1. D. Sist. Inform. y Comp. Universidad Polit\u00e9cnica de Valencia Valencia Spain."},{"key":"e_1_2_1_5_1","doi-asserted-by":"crossref","unstructured":"Hernandez V. Roman J. E. Vidal V. Verdu G. and Ginestar D. 2003. Resolution of the neutron diffusion equation with SLEPc the Scalable Library for Eigenvalue Problem Computations. In Nuclear Mathematical and Computational Sciences: A Century in Review A Century Anew. American Nuclear Society Gatlinburg TN.  Hernandez V. Roman J. E. Vidal V. Verdu G. and Ginestar D. 2003. Resolution of the neutron diffusion equation with SLEPc the Scalable Library for Eigenvalue Problem Computations. In Nuclear Mathematical and Computational Sciences: A Century in Review A Century Anew. American Nuclear Society Gatlinburg TN.","DOI":"10.1007\/3-540-36569-9_25"},{"key":"e_1_2_1_6_1","doi-asserted-by":"crossref","unstructured":"Lehoucq R. B. Sorensen D. C. and Yang C. 1998. ARPACK Users' Guide Solution of Large-Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods. SIAM Press Philadelphia PA.  Lehoucq R. B. Sorensen D. C. and Yang C. 1998. ARPACK Users' Guide Solution of Large-Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods. SIAM Press Philadelphia PA.","DOI":"10.1137\/1.9780898719628"},{"key":"e_1_2_1_7_1","volume-title":"BLZPACK: Description and user's guide. Tech. rep. TR\/PA\/95\/30","author":"Marques O. A.","year":"1995","unstructured":"Marques , O. A. 1995 . BLZPACK: Description and user's guide. Tech. rep. TR\/PA\/95\/30 . CERFACS , Toulouse, France . Marques, O. A. 1995. BLZPACK: Description and user's guide. Tech. rep. TR\/PA\/95\/30. CERFACS, Toulouse, France."},{"key":"e_1_2_1_8_1","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1002\/nla.307","article-title":"Algebraic formulations for the solution of the nullspace-free eigenvalue problem using the inexact Shift-and-Invert Lanczos method","volume":"10","author":"Simoncini V.","year":"2003","unstructured":"Simoncini , V. 2003 . Algebraic formulations for the solution of the nullspace-free eigenvalue problem using the inexact Shift-and-Invert Lanczos method . Numer. Lin. Algebra Appl. 10 , 357 -- 375 . Simoncini, V. 2003. Algebraic formulations for the solution of the nullspace-free eigenvalue problem using the inexact Shift-and-Invert Lanczos method. Numer. Lin. Algebra Appl. 10, 357--375.","journal-title":"Numer. Lin. Algebra Appl."},{"key":"e_1_2_1_9_1","doi-asserted-by":"crossref","unstructured":"Wu K. and Simon H. 1997. A parallel Lanczos method for symmetric generalized eigenvalue problems. Tech. rep. LBNL-41284. Lawrence Berkeley National Laboratory Berkeley CA.  Wu K. and Simon H. 1997. A parallel Lanczos method for symmetric generalized eigenvalue problems. Tech. rep. LBNL-41284. 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