{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,3]],"date-time":"2025-05-03T00:02:38Z","timestamp":1746230558480},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2010,6,26]],"date-time":"2010-06-26T00:00:00Z","timestamp":1277510400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2011,4]]},"DOI":"10.1007\/s11075-010-9400-2","type":"journal-article","created":{"date-parts":[[2010,6,25]],"date-time":"2010-06-25T02:36:47Z","timestamp":1277433407000},"page":"481-495","source":"Crossref","is-referenced-by-count":3,"title":["A-posteriori residual bounds for Arnoldi\u2019s methods for nonsymmetric eigenvalue problems"],"prefix":"10.1007","volume":"56","author":[{"given":"Kumar","family":"Dookhitram","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ravindra","family":"Boojhawon","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ashvin","family":"Gopaul","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muddun","family":"Bhuruth","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2010,6,26]]},"reference":[{"key":"9400_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 the matrix eigenvalue problem. Q. Appl. Math. 9, 17\u201329 (1951)","journal-title":"Q. Appl. Math."},{"key":"9400_CR2","unstructured":"Bai, Z., Barret, R., Day, D., Demmel, J., Dongarra, J.: Test Matrix Collection for Non-Hermitian Eigenvalue Problems. Technical report, Department of Mathematics, University of Kentucky, KY (1995)"},{"issue":"4","key":"9400_CR3","doi-asserted-by":"crossref","first-page":"1074","DOI":"10.1137\/S0895479801398608","volume":"25","author":"C Beattie","year":"2004","unstructured":"Beattie, C., Embree, M., Rossi, J.: Convergence of restarted Krylov subspaces to invariant subspaces. SIAM J. Matrix Anal. Appl. 25(4), 1074\u20131109 (2004)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"3","key":"9400_CR4","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1137\/S0036144503433077","volume":"47","author":"C Beattie","year":"2005","unstructured":"Beattie, C., Embree, M., Sorensen, D.C.: Convergence of polynomial restart Krylov methods for eigenvalue computations. SIAM Rev. 47(3), 492\u2013515 (2005)","journal-title":"SIAM Rev."},{"key":"9400_CR5","unstructured":"Jia, Z.: Some Numerical Methods for Large Unsymmetric Eigenproblems. PhD thesis, Mathematics Department, University of Bielefeld, Germany (1994)"},{"key":"9400_CR6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0024-3795(96)00238-8","volume":"259","author":"Z Jia","year":"1997","unstructured":"Jia, Z.: Refined iterative algorithms based on Arnoldi\u2019s process for large unsymmetric eigenproblem. Linear Algebra Appl. 259, 1\u201323 (1997)","journal-title":"Linear Algebra Appl."},{"key":"9400_CR7","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/S0024-3795(98)10197-0","volume":"287","author":"Z Jia","year":"1999","unstructured":"Jia, Z.: Polynomial characterisation of the approximate eigenvectors by the refined Arnoldi method and an implicitly restarted refined Arnoldi algorithm. Linear Algebra Appl. 287, 191\u2013214 (1999)","journal-title":"Linear Algebra Appl."},{"key":"9400_CR8","doi-asserted-by":"crossref","first-page":"255","DOI":"10.6028\/jres.045.026","volume":"45","author":"C Lanczos","year":"1950","unstructured":"Lanczos, C.: An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J. Res. Natl. Bur. Stand. 45, 255\u2013282 (1950)","journal-title":"J. Res. Natl. Bur. Stand."},{"key":"9400_CR9","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":"9400_CR10","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719628","volume-title":"ARPACK User\u2019s Guide: Solution of Large Scale Eigenvalue Problems With Implicitly Restarted Arnoldi Methods","author":"RB Lehoucq","year":"1998","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, Philadephia, PA (1998)"},{"key":"9400_CR11","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 problems. Math. Comput. 65, 1213\u20131230 (1996)","journal-title":"Math. Comput."},{"key":"9400_CR12","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1002\/(SICI)1099-1506(199801\/02)5:1<33::AID-NLA125>3.0.CO;2-1","volume":"5","author":"RB Morgan","year":"1998","unstructured":"Morgan, R.B., Zeng, M.: Harmonic projecton methods for large non-symmetric eigenvalue problems. Numer. Linear Algebr. Appl. 5, 33\u201355 (1998)","journal-title":"Numer. Linear Algebr. Appl."},{"key":"9400_CR13","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1016\/j.laa.2005.07.024","volume":"415","author":"RB Morgan","year":"2006","unstructured":"Morgan, R.B., Zeng, M.: A harmonic restarted Arnoldi for calculating eigenvalues and determining multiplicity. Linear Algebra Appl. 415, 96\u2013113 (2006)","journal-title":"Linear Algebra Appl."},{"key":"9400_CR14","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.: Variants on Arnoldi\u2019s method for computing eigenelements of large unsymmetric matrices. Linear Algebra Appl. 34, 269\u2013295 (1980)","journal-title":"Linear Algebra Appl."},{"issue":"1","key":"9400_CR15","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 J. Matrix Anal. Appl. 13(1), 357\u2013385 (1992)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9400_CR16","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1137\/S0895479800371529","volume":"23","author":"GW Stewart","year":"2001","unstructured":"Stewart, G.W.: A Krylov-Schur algorithm for large eigenproblrems. SIAM J. Matrix Anal. Appl. 23, 601\u2013614 (2001)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9400_CR17","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/0024-3795(91)90004-G","volume":"143","author":"DS Watkins","year":"1991","unstructured":"Watkins, D.S., Elsner, L.: Convergence of algorithms of decomposition type for the eigenvalue problem. Linear Algebra Appl. 143, 19\u201347 (1991)","journal-title":"Linear Algebra Appl."},{"key":"9400_CR18","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1137\/S0895479898334605","volume":"22","author":"K Wu","year":"2000","unstructured":"Wu, K., Simon, H.: Thick-restart Lanczos method for symmetric eigenvalue problems. SIAM J. Matrix Anal. Appl. 22, 602\u2013616 (2000)","journal-title":"SIAM J. Matrix Anal. Appl."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-010-9400-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-010-9400-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-010-9400-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T01:08:15Z","timestamp":1559351295000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-010-9400-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,6,26]]},"references-count":18,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2011,4]]}},"alternative-id":["9400"],"URL":"https:\/\/doi.org\/10.1007\/s11075-010-9400-2","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,6,26]]}}}