{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T21:24:34Z","timestamp":1774387474266,"version":"3.50.1"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2015,1,8]],"date-time":"2015-01-08T00:00:00Z","timestamp":1420675200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2015,10]]},"DOI":"10.1007\/s11075-014-9954-5","type":"journal-article","created":{"date-parts":[[2015,1,7]],"date-time":"2015-01-07T02:25:36Z","timestamp":1420597536000},"page":"407-426","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A key to choose subspace size in implicitly restarted Arnoldi method"],"prefix":"10.1007","volume":"70","author":[{"given":"S. A.","family":"Shahzadeh Fazeli","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nahid","family":"Emad","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zifan","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,1,8]]},"reference":[{"key":"9954_CR1","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1090\/qam\/42792","volume":"9","author":"WE Arnoldi","year":"1951","unstructured":"Arnoldi, W.E.: The Principle of Minimized Iteration in the Solution of Matrix Eigenvalue Problems. Quart. J. Appl. Math. 9, 17\u201329 (1951)","journal-title":"Quart. J. Appl. Math."},{"key":"9954_CR2","unstructured":"Bai, Z., Day, D., Demmel, J., Dongarra, J.J.: A Test Matrix Collection for Non-Hermitian Eigenvalue Problems, http:\/\/math.nist.gov\/MatrixMarket"},{"issue":"2","key":"9954_CR3","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1016\/j.cam.2009.01.009","volume":"230","author":"AH Baker","year":"2009","unstructured":"Baker, A.H., Jessup, E.R., KoleV, Tz. V.: A Simple Strategy for Varying the Restart Parameter in GMRES(M). J. Comput. Appl. Math. 230(2), 751\u2013761 (2009)","journal-title":"J. Comput. Appl. Math."},{"key":"9954_CR4","unstructured":"Chatelain, F.: Eigenvalues of matrices. Wiley (1993)"},{"key":"9954_CR5","doi-asserted-by":"crossref","unstructured":"Daniel, J.W., Gragg, W.B., Kaufman, L., Stewart, G.W.: Reorthogonalization and stable algorithms for updating the Gram-Schmidt QR factorization, Math. Comp (1976)","DOI":"10.2307\/2005398"},{"key":"9954_CR6","first-page":"387","volume":"2","author":"K Dookhitram","year":"2010","unstructured":"Dookhitram, K., Boojhawon, R., Bhuruth, M.: A new method for accelerating Arnoldi algorithms for large scale Eigenproblems. Math. Comput. Simul. 2, 387\u2013401 (2010)","journal-title":"Math. Comput. Simul."},{"key":"9954_CR7","unstructured":"Duff, I.S., Scott, J.A.: Computing selected eigenvalues of large sparse unsymmetric matrices using subspace iteration 19, 137\u2013159 (1993)"},{"issue":"1","key":"9954_CR8","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1137\/S1064827500366082","volume":"27","author":"N Emad","year":"2005","unstructured":"Emad, N., Petiton, S., Edjlali, G.: Multiple Explicitly Restarted Arnoldi Method for Solving Large Eigenproblems. SIAM J. Sci. Comput. (SJSC) 27(1), 253\u2013277 (2005)","journal-title":"SIAM J. Sci. Comput. (SJSC)"},{"issue":"2","key":"9954_CR9","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1137\/S003614450139961","volume":"45","author":"M Embree","year":"2003","unstructured":"Embree, M.: TheTortoise and the Hare Restart GMRES. SIAM Rev. 45(2), 259\u2013266 (2003)","journal-title":"SIAM Rev."},{"key":"9954_CR10","unstructured":"Lehoucq, R.B.: Analysis and Implementation of an Implicitly Restarted Iteration, PhD thesis, Rice University, Houston, Texas (1995)"},{"issue":"4","key":"9954_CR11","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1137\/S0895479895281484","volume":"17","author":"RB Lehoucq","year":"1996","unstructured":"Lehoucq, R.B., Sorensen, D.C.: Deflation techniques for an implicitly restarted Arnoldi iteration. SIAM J. Matrix Analysis and Applications 17(4), 789\u2013821 (1996)","journal-title":"SIAM J. Matrix Analysis and Applications"},{"key":"9954_CR12","doi-asserted-by":"crossref","unstructured":"Lehoucq, R.B., Sorensen, D.C., Yang, C.: ARPACK User\u2019s Guide: Solution of Large Scale Eigenvalue Problems With Implicitly Restarted Arnoldi Methods, SIAM (1998)","DOI":"10.1137\/1.9780898719628"},{"key":"9954_CR13","unstructured":"Maschhoff, K.J., Sorensen, D.C. In: Wasniewski, J., Dongarra, J., Madsen, K., D. Olesen (eds.) : Applied Parallel Computing in Industrial Problems and Optimization, volume 1184 of Lecture Notes in Computer Science. Springer-Verlag, Berlin (1996)"},{"key":"9954_CR14","doi-asserted-by":"crossref","first-page":"1213","DOI":"10.1090\/S0025-5718-96-00745-4","volume":"65","author":"RB Morgan","year":"1996","unstructured":"Morgan, R.B.: On Restarting the Arnoldi Method for Large Nonsymmetric Eigenvalue Problem. Math. Comp. 65, 1213\u20131230 (1996)","journal-title":"Math. Comp."},{"key":"9954_CR15","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1002\/1099-1506(200010\/12)7:7\/8<569::AID-NLA213>3.0.CO;2-8","volume":"7","author":"K Moriya","year":"2000","unstructured":"Moriya, K., Nodera, T.: The DEFLATED-GMRES(m, k) method with switching the restart frequency dynamically. Numer. Linear Algebra Appl. 7, 569\u2013584 (2000)","journal-title":"Numer. Linear Algebra Appl."},{"key":"9954_CR16","doi-asserted-by":"crossref","unstructured":"Parlett, B.N.: The Symmetric Eigenvalue Problem. Prentice-Hall, Inc. (1998)","DOI":"10.1137\/1.9781611971163"},{"key":"9954_CR17","unstructured":"Saad, Y.: Numerical Methods for Large Eigenvalue Problems. Manchester University Press (1993)"},{"key":"9954_CR18","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1090\/S0025-5718-1984-0736453-8","volume":"42","author":"Y Saad","year":"1984","unstructured":"Saad, Y.: Chebyshev Acceleration Techniques for Solving Nonsymmetric Eigenvalue Problems. Math. Com. 42, 567\u2013588 (1984)","journal-title":"Math. Com."},{"key":"9954_CR19","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/0024-3795(80)90169-X","volume":"34","author":"Y Saad","year":"1980","unstructured":"Saad, Y.: Variations on Arnoldi\u2019s Method for Computing Eigenelements of Large Unsymmetric Matrices. Linear Algebra Applications 34, 269\u2013295 (1980)","journal-title":"Linear Algebra Applications"},{"key":"9954_CR20","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/0010-4655(89)90149-5","volume":"53","author":"Y Saad","year":"1989","unstructured":"Saad, Y.: Numerical Solution of Large Nonsymetric Eigen Problem. Comput. Phys. Commun. 53, 71\u201390 (1989). MR 90f:65064","journal-title":"Comput. Phys. Commun."},{"key":"9954_CR21","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1137\/0613025","volume":"13","author":"DC Sorensen","year":"1992","unstructured":"Sorensen, D.C.: Implicit Application of Polynomial Filters in a k-step Arnoldi Method. SIAM Journal on Matrix Analysis and Applications 13, 357\u2013385 (1992)","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"key":"9954_CR22","doi-asserted-by":"crossref","unstructured":"Sorensen, D.C.: Implicitly Restarted Arnoldi\/Lanczos Methods for Large Scale Eigenvalue Calculations, (invited paper). Kluwer (1995)","DOI":"10.1016\/B978-044482107-2\/50003-0"},{"key":"9954_CR23","volume-title":"Parallel Numerical Algorithms, pp. 119\u2013166","author":"DC Sorensen","year":"1997","unstructured":"Sorensen, D.C.: Implicitly Restarted Arnoldi\/Lanczos Methods for Large Scale Eigenvalue Calculations. In: Keyes, D. E., Sameh, A., Venkatakrishnan, V. (eds.) Parallel Numerical Algorithms, pp. 119\u2013166. Kluwer, Dordrecht (1997)"},{"key":"9954_CR24","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1137\/S1064827596304162","volume":"19","author":"A Stathopoulos","year":"1996","unstructured":"Stathopoulos, A., Saad, Y., Wu, K.: Dynamic Thick Restarting of the Davidson, and the Implicitly Restarted Arnoldi Methods. SIAM J. Sci. Comput. 19, 227\u2013245 (1996)","journal-title":"SIAM J. Sci. Comput."},{"key":"9954_CR25","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1137\/S0895479899358595","volume":"23","author":"RB Lehoucq","year":"2001","unstructured":"Lehoucq, R.B.: Implicitly Restarted Arnoldi Methods and Subspace Iteration. SIAM J. Matrix Anal. Appl. 23, 551\u2013562 (2001)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9954_CR26","unstructured":"http:\/\/snap.stanford.edu\/data\/"},{"key":"9954_CR27","unstructured":"https:\/\/forge.prism.uvsq.fr\/projects\/miram"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-014-9954-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-014-9954-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-014-9954-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,19]],"date-time":"2019-08-19T09:23:31Z","timestamp":1566206611000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-014-9954-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1,8]]},"references-count":27,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,10]]}},"alternative-id":["9954"],"URL":"https:\/\/doi.org\/10.1007\/s11075-014-9954-5","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1,8]]}}}