{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T21:20:17Z","timestamp":1774387217626,"version":"3.50.1"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2015,4,2]],"date-time":"2015-04-02T00:00:00Z","timestamp":1427932800000},"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":[[2016,1]]},"DOI":"10.1007\/s11075-015-9987-4","type":"journal-article","created":{"date-parts":[[2015,4,1]],"date-time":"2015-04-01T11:14:50Z","timestamp":1427886890000},"page":"103-120","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Error bounds of Rayleigh\u2013Ritz type contour integral-based eigensolver for solving generalized eigenvalue problems"],"prefix":"10.1007","volume":"71","author":[{"given":"Akira","family":"Imakura","sequence":"first","affiliation":[]},{"given":"Lei","family":"Du","sequence":"additional","affiliation":[]},{"given":"Tetsuya","family":"Sakurai","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,4,2]]},"reference":[{"key":"9987_CR1","doi-asserted-by":"crossref","first-page":"52","DOI":"10.14495\/jsiaml.1.52","volume":"1","author":"J Asakura","year":"2009","unstructured":"Asakura, J., Sakurai, T., Tadano, H., Ikegami, T., Kimura, K.: A numerical method for nonlinear eigenvalue problems using contour integrals. JSIAM Lett. 1, 52\u201355 (2009)","journal-title":"JSIAM Lett."},{"key":"9987_CR2","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/s13160-010-0005-x","volume":"27","author":"J Asakura","year":"2010","unstructured":"Asakura, J., Sakurai, T., Tadano, H., Ikegami, T., Kimura, K.: A numerical method for polynomial eigenvalue problems using contour integral. Jpn. J. Indust. Appl. Math 27, 73\u201390 (2010)","journal-title":"Jpn. J. Indust. Appl. Math"},{"key":"9987_CR3","doi-asserted-by":"crossref","first-page":"3839","DOI":"10.1016\/j.laa.2011.03.030","volume":"436","author":"W-J Beyn","year":"2012","unstructured":"Beyn, W.-J.: An integral method for solving nonlinear eigenvalue problems. Lin. Alg. Appl. 436, 3839\u20133863 (2012)","journal-title":"Lin. Alg. Appl."},{"key":"9987_CR4","volume-title":"Eigenvalues of Matrices","author":"F Chatelin","year":"1993","unstructured":"Chatelin, F.: Eigenvalues of Matrices. Wiley, Chichester (1993)"},{"key":"9987_CR5","first-page":"420","volume-title":"Modern Mathematical Models, Methods and Algorithms for Real World Systems","author":"MH Gutknecht","year":"2007","unstructured":"Gutknecht, M.H.: Block Krylov space methods for linear systems with multiple right-hand sides: an introduction. In: Siddiqi, A.H., Duff, I.S., Christensen, O. (eds.) Modern Mathematical Models, Methods and Algorithms for Real World Systems, pp. 420\u2013447. Anamaya Publishers, New Delhi (2007)"},{"key":"9987_CR6","doi-asserted-by":"crossref","first-page":"1927","DOI":"10.1016\/j.cam.2009.09.029","volume":"233","author":"T Ikegami","year":"2010","unstructured":"Ikegami, T., Sakurai, T., Nagashima, U.: A filter diagonalization for generalized eigenvalue problems based on the Sakurai-Sugiura projection method. J. Comput. Appl. Math. 233, 1927\u20131936 (2010)","journal-title":"J. Comput. Appl. Math."},{"key":"9987_CR7","doi-asserted-by":"crossref","first-page":"825","DOI":"10.11650\/twjm\/1500405869","volume":"14","author":"T Ikegami","year":"2010","unstructured":"Ikegami, T., Sakurai, T.: Contour integral eigensolver for non-Hermitian systems: a Rayleigh-Ritz-type approach. Taiwan. J. Math. 14, 825\u2013837 (2010)","journal-title":"Taiwan. J. Math."},{"key":"9987_CR8","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1016\/j.aml.2014.02.007","volume":"32","author":"A Imakura","year":"2014","unstructured":"Imakura, A., Du, L., Sakurai, T.: A block Arnoldi-type contour integral spectral projection method for solving generalized eigenvalue problems. Appl. Math. Lett. 32, 22\u201327 (2014)","journal-title":"Appl. Math. Lett."},{"key":"9987_CR9","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1023\/A:1022387106878","volume":"39","author":"P Kravanja","year":"1999","unstructured":"Kravanja, P., Sakurai, T., van Barel, M.: On locating clusters of zeros of analytic functions. BIT 39, 646\u2013682 (1999)","journal-title":"BIT"},{"key":"9987_CR10","unstructured":"Matrix Market. http:\/\/math.nist.gov\/MatrixMarket\/"},{"key":"9987_CR11","doi-asserted-by":"crossref","unstructured":"Polizzi, E.: A density matrix-based algorithm for solving eigenvalue problems, vol. 79 (2009)","DOI":"10.1103\/PhysRevB.79.115112"},{"key":"9987_CR12","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970739","volume-title":"Numerical Methods for Large Eigenvalue Problems 2nd edition","author":"Y Saad","year":"2011","unstructured":"Saad, Y.: Numerical Methods for Large Eigenvalue Problems 2nd edition. SIAM, Philadelphia, PA (2011)"},{"key":"9987_CR13","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1016\/S0377-0427(02)00724-0","volume":"152","author":"T Sakurai","year":"2003","unstructured":"Sakurai, T., Kravanja, P., Sugiura, H., van Barel, M.: An error analysis of two related quadrature methods for computing zeros of analytic functions. J. Comput. Appl. Math. 152, 467\u2013480 (2003)","journal-title":"J. Comput. Appl. Math."},{"key":"9987_CR14","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/S0377-0427(03)00565-X","volume":"159","author":"T Sakurai","year":"2003","unstructured":"Sakurai, T., Sugiura, H.: A projection method for generalized eigenvalue problems using numerical integration. J. Comput. Appl. Math. 159, 119\u2013128 (2003)","journal-title":"J. Comput. Appl. Math."},{"key":"9987_CR15","doi-asserted-by":"crossref","first-page":"745","DOI":"10.14492\/hokmj\/1272848031","volume":"36","author":"T Sakurai","year":"2007","unstructured":"Sakurai, T., Tadano, H.: CIRR: a Rayleigh-Ritz type method with contour integral for generalized eigenvalue problems. Hokkaido Math. J. 36, 745\u2013757 (2007)","journal-title":"Hokkaido Math. J."},{"key":"9987_CR16","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1016\/j.cpc.2011.11.005","volume":"183","author":"G Schofield","year":"2012","unstructured":"Schofield, G., Chelikowsky, J.R., Saad, Y.: A spectrum slicing method for the Kohn-Sham problem. Comput. Phys. Commun. 183, 497\u2013505 (2012)","journal-title":"Comput. Phys. Commun."},{"key":"9987_CR17","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1137\/13090866X","volume":"35","author":"PTP Tang","year":"2014","unstructured":"Tang, P.T.P., Polizzi, E.: FEAST as a subspace iteration eigensolver accelerated by approximate spectral projection. SIAM. J. Matrix Anal. Appl. 35, 354\u2013390 (2014)","journal-title":"J. Matrix Anal. Appl."},{"key":"9987_CR18","doi-asserted-by":"crossref","first-page":"41","DOI":"10.14495\/jsiaml.5.41","volume":"5","author":"S Yokota","year":"2013","unstructured":"Yokota, S., Sakurai, T.: A projection method for nonlinear eigenvalue problems using contour integrals. JSIAM Lett. 5, 41\u201344 (2013)","journal-title":"JSIAM Lett."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-015-9987-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-015-9987-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-015-9987-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,22]],"date-time":"2019-08-22T14:46:39Z","timestamp":1566485199000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-015-9987-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4,2]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,1]]}},"alternative-id":["9987"],"URL":"https:\/\/doi.org\/10.1007\/s11075-015-9987-4","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,4,2]]}}}