{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T17:23:14Z","timestamp":1777915394991,"version":"3.51.4"},"reference-count":22,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2010,9,1]],"date-time":"2010-09-01T00:00:00Z","timestamp":1283299200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000121","name":"Division of Mathematical Sciences","doi-asserted-by":"publisher","award":["DMS-0611548OCI-0749217"],"award-info":[{"award-number":["DMS-0611548OCI-0749217"]}],"id":[{"id":"10.13039\/100000121","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-AC02-05CH11231"],"award-info":[{"award-number":["DE-AC02-05CH11231"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"publisher","award":["DE-FC02-06ER25794"],"award-info":[{"award-number":["DE-FC02-06ER25794"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000105","name":"Office of Cyberinfrastructure","doi-asserted-by":"publisher","award":["DMS-0611548OCI-0749217"],"award-info":[{"award-number":["DMS-0611548OCI-0749217"]}],"id":[{"id":"10.13039\/100000105","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[2010,9]]},"abstract":"<jats:p>\n            The Thick-Restart Lanczos (TRLan) method is an effective method for solving large-scale Hermitian eigenvalue problems. The performance of the method strongly depends on the dimension of the projection subspace used at each restart. In this article, we propose an objective function to quantify the effectiveness of the selection of subspace dimension, and then introduce an adaptive scheme to dynamically select the dimension to optimize the performance. We have developed an open-source software package\n            <jats:italic>a<\/jats:italic>\n            --TRLan to include this adaptive scheme in the TRLan method. When applied to calculate the electronic structure of quantum dots,\n            <jats:italic>a<\/jats:italic>\n            --TRLan runs up to 2.3x faster than a state-of-the-art preconditioned conjugate gradient eigensolver.\n          <\/jats:p>","DOI":"10.1145\/1824801.1824805","type":"journal-article","created":{"date-parts":[[2010,9,28]],"date-time":"2010-09-28T17:41:41Z","timestamp":1285695701000},"page":"1-18","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":30,"title":["Adaptive Projection Subspace Dimension for the Thick-Restart Lanczos Method"],"prefix":"10.1145","volume":"37","author":[{"given":"Ichitaro","family":"Yamazaki","sequence":"first","affiliation":[{"name":"University of California, Davis"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhaojun","family":"Bai","sequence":"additional","affiliation":[{"name":"University of California, Davis"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Horst","family":"Simon","sequence":"additional","affiliation":[{"name":"Lawrence Berkeley National Laboratory"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lin-Wang","family":"Wang","sequence":"additional","affiliation":[{"name":"Lawrence Berkeley National Laboratory"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kesheng","family":"Wu","sequence":"additional","affiliation":[{"name":"Lawrence Berkeley National Laboratory"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2010,9]]},"reference":[{"key":"e_1_2_1_1_1","first-page":"1","article-title":"An implicitly restarted Lanczos method for large symmetric eigenvalue problems. Electro","volume":"2","author":"Calvetti D.","year":"1994","journal-title":"Trans. Numer. Anal."},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2000.6440"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1137\/0915004"},{"key":"e_1_2_1_4_1","doi-asserted-by":"crossref","unstructured":"}}Demmel J. W. 1997. Applied Numerical Linear Algebra. SIAM Philadelphia PA.   }} Demmel J. W. 1997. Applied Numerical Linear Algebra . SIAM Philadelphia PA.","DOI":"10.1137\/1.9781611971446"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.6028\/jres.045.026"},{"key":"e_1_2_1_6_1","doi-asserted-by":"crossref","unstructured":"}}Lehoucq R. Sorensen D. and Yang C. 1998. ARPACK Users Guide: Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. SIAM Philadelphia PA. Software http:\/\/www.caam.rice.edu\/software\/ARPACK\/.  }} Lehoucq R. Sorensen D. and Yang C. 1998. ARPACK Users Guide: Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods . SIAM Philadelphia PA. Software http:\/\/www.caam.rice.edu\/software\/ARPACK\/.","DOI":"10.1137\/1.9780898719628"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1737470"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-96-00745-4"},{"key":"e_1_2_1_9_1","doi-asserted-by":"crossref","unstructured":"}}Parlett B. N. 1998. The Symmetric Eigenvalue Problem. Classics in Applied Mathematics. SIAM Philadelphia PA.   }} Parlett B. N. 1998. The Symmetric Eigenvalue Problem. Classics in Applied Mathematics. SIAM Philadelphia PA.","DOI":"10.1137\/1.9781611971163"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.64.1045"},{"key":"e_1_2_1_11_1","unstructured":"}}Saad Y. 1993. Numerical Methods for Large Eigenvalue Problems. Manchester University Press Manchester UK.  }} Saad Y. 1993. Numerical Methods for Large Eigenvalue Problems . Manchester University Press Manchester UK."},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.73.245332"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1137\/0613025"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1137\/060661910"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827596304162"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2008.01.018"},{"key":"e_1_2_1_17_1","unstructured":"}}Wang L. Canning A. Marques O. and Voemel C. 2008. The parallel energy scan (PESCAN) code. http:\/\/icl.cs.utk.edu\/doe-nano\/software\/pescan\/escan.  }} Wang L. Canning A. Marques O. and Voemel C. 2008. The parallel energy scan (PESCAN) code. http:\/\/icl.cs.utk.edu\/doe-nano\/software\/pescan\/escan."},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.466486"},{"key":"e_1_2_1_19_1","doi-asserted-by":"crossref","unstructured":"}}Wang L. and Zunger A. 1996. Pseudopotential theory of nanometer silicon quantum dots application to silicon quantum dots. In Semiconductor Nanocluster P. Kamat and D. Meisel Eds. ACM New York NY 161--207.  }} Wang L. and Zunger A. 1996. Pseudopotential theory of nanometer silicon quantum dots application to silicon quantum dots. In Semiconductor Nanocluster P. Kamat and D. Meisel Eds. ACM New York NY 161--207.","DOI":"10.1016\/S0167-2991(97)81103-2"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479898334605"},{"key":"e_1_2_1_21_1","doi-asserted-by":"crossref","unstructured":"}}Wu K. and Simon H. 2000b. TRLan user guide. Tech. rep. LBNL-43178 Lawrence Berkeley National Laboratory. Software http:\/\/crd.lbl.gov\/~kewu\/trlan.html.  }} Wu K. and Simon H. 2000b. TRLan user guide. Tech. rep. LBNL-43178 Lawrence Berkeley National Laboratory. Software http:\/\/crd.lbl.gov\/~kewu\/trlan.html.","DOI":"10.2172\/6539"},{"key":"e_1_2_1_22_1","unstructured":"}}Yamazaki I. Wu K. and Simon H. 2008. a--TRLan user guide. Tech. rep. LBNL-1288E Lawrence Berkeley National Laboratory. Software https:\/\/codeforge.lbl.gov\/projects\/trlan\/.  }} Yamazaki I. Wu K. and Simon H. 2008. a --TRLan user guide. Tech. rep. LBNL-1288E Lawrence Berkeley National Laboratory. Software https:\/\/codeforge.lbl.gov\/projects\/trlan\/."}],"container-title":["ACM Transactions on Mathematical Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1824801.1824805","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1824801.1824805","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T11:39:54Z","timestamp":1750246794000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1824801.1824805"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,9]]},"references-count":22,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,9]]}},"alternative-id":["10.1145\/1824801.1824805"],"URL":"https:\/\/doi.org\/10.1145\/1824801.1824805","relation":{},"ISSN":["0098-3500","1557-7295"],"issn-type":[{"value":"0098-3500","type":"print"},{"value":"1557-7295","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,9]]},"assertion":[{"value":"2008-09-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2010-02-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2010-09-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}