{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T16:03:18Z","timestamp":1775145798288,"version":"3.50.1"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2014,2,25]],"date-time":"2014-02-25T00:00:00Z","timestamp":1393286400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2015,5]]},"DOI":"10.1007\/s11222-014-9454-4","type":"journal-article","created":{"date-parts":[[2014,2,24]],"date-time":"2014-02-24T10:32:20Z","timestamp":1393237940000},"page":"561-577","source":"Crossref","is-referenced-by-count":27,"title":["An efficient implementation of the ensemble Kalman filter based on an iterative Sherman\u2013Morrison formula"],"prefix":"10.1007","volume":"25","author":[{"given":"Elias D.","family":"Nino Ruiz","sequence":"first","affiliation":[]},{"given":"Adrian","family":"Sandu","sequence":"additional","affiliation":[]},{"given":"Jeffrey","family":"Anderson","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,2,25]]},"reference":[{"key":"9454_CR1","doi-asserted-by":"crossref","first-page":"3643","DOI":"10.1256\/qj.05.113","volume":"131","author":"O Alves","year":"2005","unstructured":"Alves, O., Robert, C.: Tropical Pacific Ocean model error covariances from Monte Carlo simulations. Q. J. R. Meteorol. Soc. 131, 3643\u20133658 (2005)","journal-title":"Q. J. R. Meteorol. Soc."},{"issue":"12","key":"9454_CR2","doi-asserted-by":"crossref","first-page":"2884","DOI":"10.1175\/1520-0493(2001)129<2884:AEAKFF>2.0.CO;2","volume":"129","author":"JL Anderson","year":"2001","unstructured":"Anderson, J.L.: An ensemble adjustment Kalman filter for data assimilation. Mon. Weather Rev. 129(12), 2884\u20132903 (2001)","journal-title":"Mon. Weather Rev."},{"issue":"1\u20132","key":"9454_CR3","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.physd.2006.02.011","volume":"230","author":"JL Anderson","year":"2007","unstructured":"Anderson, J.L.: Exploring the need for localization in ensemble data assimilation using a hierarchical ensemble filter. Physica D Nonlinear Phenomena 230(1\u20132), 99\u2013111 (2007)","journal-title":"Physica D Nonlinear Phenomena"},{"issue":"8","key":"9454_CR4","doi-asserted-by":"crossref","first-page":"1452","DOI":"10.1175\/JTECH2049.1","volume":"24","author":"JL Anderson","year":"2007","unstructured":"Anderson, J.L., Collins, N.: Scalable implementations of ensemble filter algorithms for data assimilation. J. Atmos. Ocean. Technol. 24(8), 1452\u20131463 (2007)","journal-title":"J. Atmos. Ocean. Technol."},{"key":"9454_CR5","doi-asserted-by":"crossref","unstructured":"Angerson, E., Bai, Z., Dongarra, J., Greenbaum, A., McKenney, A., Du Croz, J., Hammarling, S., Demmel, J., Bischof, C., Sorensen, D.: Lapack: A portable linear algebra library for high-performance computers. In: Proceedings of Supercomputing 1990. pp. 2\u201311 (1990). doi: 10.1109\/SUPERC.1990.129995","DOI":"10.1109\/SUPERC.1990.129995"},{"key":"9454_CR6","doi-asserted-by":"crossref","unstructured":"Carton, X., Baraille, R.: Data assimilation in quasi-geostrophic ocean models. In: Proceedings of OCEANS 94. Oceans Engineering for Today\u2019s Technology and Tomorrow\u2019s Preservation. vol. 3, pp. III\/337\u2013III\/346 (1994). doi: 10.1109\/OCEANS.1994.364221","DOI":"10.1109\/OCEANS.1994.364221"},{"issue":"2","key":"9454_CR7","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1137\/0709024","volume":"9","author":"A Cohen","year":"1972","unstructured":"Cohen, A.: Rate of convergence of several conjugate gradient algorithms. SIAM J. Numer. Anal. 9(2), 248\u2013259 (1972)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"9454_CR8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/0902001","volume":"2","author":"S Eisenstat","year":"1981","unstructured":"Eisenstat, S.: Efficient implementation of a class of preconditioned conjugate gradient methods. SIAM J. Sci. Stat. Comput. 2(1), 1\u20134 (1981)","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"9454_CR9","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-03711-5","volume-title":"Data Assimilation: The Ensemble Kalman Filter","author":"G Evensen","year":"2009","unstructured":"Evensen, G.: Chap. 14. Data Assimilation: The Ensemble Kalman Filter, 2nd edn. Springer, New York (2009)","edition":"2"},{"key":"9454_CR10","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/978-3-642-03711-5_17","volume-title":"Data Assimilation","author":"G Evensen","year":"2009","unstructured":"Evensen, G.: Estimation in an oil reservoir simulator. Data Assimilation, pp. 263\u2013272. Springer, Berlin (2009)"},{"issue":"3","key":"9454_CR11","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1109\/MCS.2009.932223","volume":"29","author":"G Evensen","year":"2009","unstructured":"Evensen, G.: The ensemble Kalman filter for combined state and parameter estimation. Control Syst. IEEE 29(3), 83\u2013104 (2009)","journal-title":"Control Syst. IEEE"},{"key":"9454_CR12","doi-asserted-by":"crossref","unstructured":"Fraser, A.M.: Hidden Markov models and dynamical systems. SIAM (2008). doi: 10.1137\/1.9780898717747","DOI":"10.1137\/1.9780898717747"},{"issue":"1","key":"9454_CR13","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1137\/S0895479893252623","volume":"17","author":"P Gill","year":"1996","unstructured":"Gill, P., Saunders, M., Shinnerl, J.: On the stability of Cholesky factorization for symmetric quasidefinite systems. SIAM J. Matrix Anal. Appl. 17(1), 35\u201346 (1996)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"3","key":"9454_CR14","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1007\/s10596-011-9268-9","volume":"16","author":"H Godinez","year":"2012","unstructured":"Godinez, H., Moulton, J.: An efficient matrix-free algorithm for the ensemble Kalman filter. Comput. Geosci. 16(3), 565\u2013575 (2012). doi: 10.1007\/s10596-011-9268-9","journal-title":"Comput. Geosci."},{"issue":"1","key":"9454_CR15","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1137\/1031003","volume":"31","author":"G Golub","year":"1989","unstructured":"Golub, G., OLeary, D.: Some history of the conjugate gradient and Lanczos algorithms: 1948\u20131976. SIAM Rev. 31(1), 50\u2013102 (1989)","journal-title":"SIAM Rev."},{"key":"9454_CR16","doi-asserted-by":"crossref","first-page":"382","DOI":"10.2118\/102430-PA","volume":"13","author":"V Haugen","year":"2008","unstructured":"Haugen, V., Naevdal, G., Natvik, L.J., Evensen, G., Berg, A., Flornes, K.: History matching using the ensemble Kalman filter on a north sea field case. SPE J. 13, 382\u2013391 (2008)","journal-title":"SPE J."},{"issue":"4","key":"9454_CR17","doi-asserted-by":"crossref","first-page":"1275","DOI":"10.1137\/100793876","volume":"32","author":"A Kovalenko","year":"2011","unstructured":"Kovalenko, A., Mannseth, T., N\u00e6vdal, G.: Error estimate for the ensemble Kalman filter analysis step. SIAM J. Matrix Anal. Appl. 32(4), 1275\u20131287 (2011)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"639","key":"9454_CR18","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1002\/qj.371","volume":"135","author":"H Li","year":"2009","unstructured":"Li, H., Kalnay, E., Miyoshi, T.: Simultaneous estimation of covariance inflation and observation errors within an ensemble Kalman filter. Q. J. R. Meteorol. Soc. 135(639), 523\u2013533 (2009). doi: 10.1002\/qj.371","journal-title":"Q. J. R. Meteorol. Soc."},{"issue":"1","key":"9454_CR19","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1137\/S1064827597327334","volume":"21","author":"C Lin","year":"1999","unstructured":"Lin, C., More, J.: Incomplete Cholesky factorizations with limited memory. SIAM J. Sci. Comput. 21(1), 24\u201345 (1999). doi: 10.1137\/S1064827597327334","journal-title":"SIAM J. Sci. Comput."},{"key":"9454_CR20","unstructured":"Mandel, J.: Efficient implementation of the ensemble Kalman filter. University of Colorado at Denver and Health Sciences Center, Technical Report (2006)"},{"issue":"2\u20133","key":"9454_CR21","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1016\/j.laa.2006.07.007","volume":"420","author":"P Maponi","year":"2007","unstructured":"Maponi, P.: The solution of linear systems by using the Sherman\u2013Morrison formula. Linear Algebra Appl. 420(2\u20133), 276\u2013294 (2007). doi: 10.1016\/j.laa.2006.07.007","journal-title":"Linear Algebra Appl."},{"key":"9454_CR22","unstructured":"Meinguet, J.: Refined error analyses of Cholesky factorization. SIAM J. Numer. Anal. 20(6), 1243\u20131250 (1983)"},{"key":"9454_CR23","doi-asserted-by":"crossref","unstructured":"Ott, E., Hunt, B.R., Szunyogh, I., Zimin, A.V., Kostelich, E.J., Corazza, M., Kalnay, E., Patil, D.J., Yorke, J.A.: A local ensemble Kalman filter for atmospheric data assimilation. Tellus A 56(5), 415\u2013428 (2004)","DOI":"10.1111\/j.1600-0870.2004.00076.x"},{"issue":"1","key":"9454_CR24","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1137\/S0895479897316588","volume":"21","author":"K Otto","year":"1999","unstructured":"Otto, K., Larsson, E.: Iterative solution of the Helmholtz equation by a second-order method. SIAM J. Matrix Anal. Appl. 21(1), 209\u2013229 (1999). doi: 10.1137\/S0895479897316588","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"2","key":"9454_CR25","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1137\/0709032","volume":"9","author":"J Reid","year":"1972","unstructured":"Reid, J.: The use of conjugate gradients for systems of linear equations possessing property A. SIAM J. Numer. Anal. 9(2), 325\u2013332 (1972)","journal-title":"SIAM J. Numer. Anal."},{"issue":"6","key":"9454_CR26","doi-asserted-by":"crossref","first-page":"1136","DOI":"10.1137\/0911064","volume":"11","author":"R Schnabel","year":"1990","unstructured":"Schnabel, R., Eskow, E.: A new modified Cholesky factorization. SIAM J. Sci. Stat. Comput. 11(6), 1136\u20131158 (1990). doi: 10.1137\/0911064","journal-title":"SIAM J. Sci. Stat. Comput."},{"issue":"1","key":"9454_CR27","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1137\/S089547989528692X","volume":"18","author":"M Stewart","year":"1997","unstructured":"Stewart, M., Van Dooren, P.: Stability issues in the factorization of structured matrices. SIAM J. Matrix Anal. Appl. 18(1), 104\u2013118 (1997)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9454_CR28","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1175\/WAF-D-11-00030.1","volume":"27","author":"A Suarez","year":"2012","unstructured":"Suarez, A., Heather Dawn, R., Dustan, W., Coniglio, M.: Comparison of ensemble Kalman filter-based forecasts to traditional ensemble and deterministic forecasts for a case study of banded snow. Weather Forecast. 27, 85\u2013105 (2012)","journal-title":"Weather Forecast."},{"issue":"7","key":"9454_CR29","doi-asserted-by":"crossref","first-page":"1485","DOI":"10.1175\/1520-0493(2003)131<1485:ESRF>2.0.CO;2","volume":"131","author":"MK Tippett","year":"2003","unstructured":"Tippett, M.K., Anderson, J.L., Bishop, C.H., Hamill, T.M., Whitaker, J.S.: Ensemble square root filters. Mon. Weather Rev. 131(7), 1485\u20131490 (2003)","journal-title":"Mon. Weather Rev."},{"key":"9454_CR30","unstructured":"Wu, G., Zheng, X., Li, Y.: Inflation adjustment on error covariance matrix of ensemble Kalman filter. In: International Conference on Multimedia Technology (ICMT), 2011. pp. 2160\u20132163 (2011)"},{"issue":"5","key":"9454_CR31","doi-asserted-by":"crossref","first-page":"2899","DOI":"10.1137\/090750500","volume":"31","author":"J Xia","year":"2010","unstructured":"Xia, J., Gu, M.: Robust approximate Cholesky factorization of rank-structured symmetric positive definite matrices. SIAM J. Matrix Anal. Appl. 31(5), 2899\u20132920 (2010). doi: 10.1137\/090750500","journal-title":"SIAM J. Matrix Anal. Appl."}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-014-9454-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11222-014-9454-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-014-9454-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T22:31:52Z","timestamp":1565217112000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11222-014-9454-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,2,25]]},"references-count":31,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,5]]}},"alternative-id":["9454"],"URL":"https:\/\/doi.org\/10.1007\/s11222-014-9454-4","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"value":"0960-3174","type":"print"},{"value":"1573-1375","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,2,25]]}}}