{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T17:00:20Z","timestamp":1782234020341,"version":"3.54.5"},"reference-count":33,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2018,10,1]],"date-time":"2018-10-01T00:00:00Z","timestamp":1538352000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2018,3,14]],"date-time":"2018-03-14T00:00:00Z","timestamp":1520985600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"name":"Austrian Science FundAustrian Science Fund (FWF)","award":["P27926"],"award-info":[{"award-number":["P27926"]}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Applied Mathematics"],"published-print":{"date-parts":[[2018,10]]},"DOI":"10.1016\/j.cam.2018.01.035","type":"journal-article","created":{"date-parts":[[2018,3,16]],"date-time":"2018-03-16T21:01:59Z","timestamp":1521234119000},"page":"602-614","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":26,"special_numbering":"C","title":["Numerical low-rank approximation of matrix differential equations"],"prefix":"10.1016","volume":"340","author":[{"given":"Hermann","family":"Mena","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexander","family":"Ostermann","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lena-Maria","family":"Pfurtscheller","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chiara","family":"Piazzola","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.cam.2018.01.035_b1","series-title":"Matrix Riccati Equations in Control and Systems Theory","author":"Abou-Kandil","year":"2003"},{"key":"10.1016\/j.cam.2018.01.035_b2","series-title":"Approximation of Large-Scale Dynamical Systems","author":"Antoulas","year":"2005"},{"key":"10.1016\/j.cam.2018.01.035_b3","series-title":"Robust Control Design Using H\u221e Methods","author":"Petersen","year":"2000"},{"key":"10.1016\/j.cam.2018.01.035_b4","doi-asserted-by":"crossref","first-page":"770","DOI":"10.1109\/9.57015","article-title":"Efficient matrix-valued algorithms for solving stiff Riccati differential equations","volume":"35","author":"Choi","year":"1990","journal-title":"IEEE Trans. Automat. Control"},{"key":"10.1016\/j.cam.2018.01.035_b5","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1137\/0729049","article-title":"Numerical integration of the differential Riccati equation and some related issues","volume":"29","author":"Dieci","year":"1992","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.cam.2018.01.035_b6","doi-asserted-by":"crossref","first-page":"2950","DOI":"10.1109\/TAC.2013.2258495","article-title":"Rosenbrock methods for solving differential Riccati equations","volume":"58","author":"Benner","year":"2013","journal-title":"IEEE Trans. Automat. Control"},{"key":"10.1016\/j.cam.2018.01.035_b7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1515\/jnma-2016-1039","article-title":"Numerical solution of the infinite-dimensional LQR problem and the associated Riccati differential equations","volume":"26","author":"Benner","year":"2018","journal-title":"J. Numer. Math."},{"key":"10.1016\/j.cam.2018.01.035_b8","doi-asserted-by":"crossref","first-page":"2791","DOI":"10.1109\/TAC.2015.2398889","article-title":"Low-rank second-order splitting of large-scale differential Riccati equations","volume":"60","author":"Stillfjord","year":"2015","journal-title":"IEEE Trans. Automat. Control"},{"key":"10.1016\/j.cam.2018.01.035_b9","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1137\/050639703","article-title":"Dynamical low-rank approximation","volume":"29","author":"Koch","year":"2007","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"10.1016\/j.cam.2018.01.035_b10","doi-asserted-by":"crossref","first-page":"1020","DOI":"10.1137\/15M1026791","article-title":"Discretized dynamical low-rank approximation in the presence of small singular values","volume":"54","author":"Kieri","year":"2016","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.cam.2018.01.035_b11","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/s10543-013-0454-0","article-title":"A projector-splitting integrator for dynamical low-rank approximation","volume":"54","author":"Lubich","year":"2014","journal-title":"BIT"},{"key":"10.1016\/j.cam.2018.01.035_b12","doi-asserted-by":"crossref","first-page":"1346","DOI":"10.1016\/j.matcom.2008.03.007","article-title":"Dynamical low-rank approximation: applications and numerical experiments","volume":"79","author":"Nonnenmacher","year":"2008","journal-title":"Math. Comput. Simulation"},{"key":"10.1016\/j.cam.2018.01.035_b13","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/S0167-6911(02)00147-0","article-title":"On the decay rate of Hankel singular values and related issues","volume":"46","author":"Antoulas","year":"2000","journal-title":"Systems Control Lett."},{"key":"10.1016\/j.cam.2018.01.035_b14","series-title":"Solution of Large-Scale Lyapunov Equations via the Block Modified Smith Method","author":"Sabino","year":"2007"},{"key":"10.1016\/j.cam.2018.01.035_b15","doi-asserted-by":"crossref","first-page":"A1639","DOI":"10.1137\/15M1027620","article-title":"The Leja method revisited: backward error analysis for the matrix exponential","volume":"38","author":"Caliari","year":"2016","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.cam.2018.01.035_b16","series-title":"Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations","author":"Hairer","year":"2000"},{"key":"10.1016\/j.cam.2018.01.035_b17","series-title":"Optimization and Dynamical Systems","author":"Helmke","year":"1996"},{"key":"10.1016\/j.cam.2018.01.035_b18","doi-asserted-by":"crossref","first-page":"488","DOI":"10.1137\/100788860","article-title":"Computing the action of the matrix exponential, with an application to exponential integrators","volume":"33","author":"Al-Mohy","year":"2011","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.cam.2018.01.035_b19","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1002\/gamm.201310002","article-title":"Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection","volume":"36","author":"G\u00fcttel","year":"2013","journal-title":"GAMM-Mitt"},{"key":"10.1016\/j.cam.2018.01.035_b20","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1137\/0729014","article-title":"Analysis of some Krylov subspace approximations to the matrix exponential operator","volume":"29","author":"Saad","year":"1992","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.cam.2018.01.035_b21","series-title":"Solving Ordinary Differential Equations I: Nonstiff Problems","author":"Hairer","year":"1993"},{"key":"10.1016\/j.cam.2018.01.035_b22","doi-asserted-by":"crossref","first-page":"A1577","DOI":"10.1137\/140994204","article-title":"Overcoming order reduction in diffusion-reaction splitting. Part 1: Dirichlet boundary conditions","volume":"37","author":"Einkemmer","year":"2015","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.cam.2018.01.035_b23","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/0024-3795(88)90223-6","article-title":"Computing a nearest symmetric positive semidefinite matrix","volume":"103","author":"Higham","year":"1988","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/j.cam.2018.01.035_b24","doi-asserted-by":"crossref","first-page":"1268","DOI":"10.1137\/06066120X","article-title":"A new iterative method for solving large-scale Lyapunov matrix equations","volume":"29","author":"Simoncini","year":"2007","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.cam.2018.01.035_b25","article-title":"A simple predictive model for El Ni\u00f1o","volume":"42","author":"Case","year":"2009","journal-title":"SIAM News"},{"key":"10.1016\/j.cam.2018.01.035_b26","doi-asserted-by":"crossref","first-page":"1999","DOI":"10.1175\/1520-0442(1995)008<1999:TOGOTS>2.0.CO;2","article-title":"The optimal growth of tropical sea surface temperature anomalies","volume":"8","author":"Penland","year":"1995","journal-title":"J. Clim."},{"key":"10.1016\/j.cam.2018.01.035_b27","unstructured":"National Climatic Data Center, NESDIS, NOAA, U.S. Department of Commerce, NOAA Optimum Interpolation 1\/4 Degree Daily Sea Surface Temperature Analysis, Version 2, http:\/\/rda.ucar.edu\/datasets\/ds277.7\/. (Accessed 16 February 2016)."},{"key":"10.1016\/j.cam.2018.01.035_b28","unstructured":"ESR, 2009. OSCAR third degree resolution ocean surface currents. Ver. 1. PO.DAAC, CA, USA, http:\/\/dx.doi.org\/10.5067\/OSCAR-03D01. (Accessed 30 May 2016)."},{"key":"10.1016\/j.cam.2018.01.035_b29","unstructured":"H. Mena, L. Pfurtscheller, An efficient SPDE approach for El Ni\u00f1o, arXiv, 2017, https:\/\/arxiv.org\/abs\/1708.04144."},{"key":"10.1016\/j.cam.2018.01.035_b30","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/s002110050030","article-title":"Positive definiteness in the numerical solution of Riccati differential equations","volume":"67","author":"Dieci","year":"1994","journal-title":"Numer. Math."},{"key":"10.1016\/j.cam.2018.01.035_b31","series-title":"LYAPACK Users Guide, Technical Report SFB393\/00-33","author":"Penzl","year":"2000"},{"key":"10.1016\/j.cam.2018.01.035_b32","series-title":"Stochastic Controls. Hamiltonian Systems and HJB Equations","author":"Yong","year":"1999"},{"key":"10.1016\/j.cam.2018.01.035_b33","doi-asserted-by":"crossref","first-page":"e2091","DOI":"10.1002\/nla.2091","article-title":"Numerical solution of the finite horizon stochastic linear quadratic control problem","volume":"24","author":"Damm","year":"2017","journal-title":"Numer. Linear Algebra Appl."}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042718301201?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042718301201?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,6,12]],"date-time":"2019-06-12T06:57:54Z","timestamp":1560322674000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377042718301201"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10]]},"references-count":33,"alternative-id":["S0377042718301201"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2018.01.035","relation":{},"ISSN":["0377-0427"],"issn-type":[{"value":"0377-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2018,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Numerical low-rank approximation of matrix differential equations","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational and Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cam.2018.01.035","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2018 The Author(s). Published by Elsevier B.V.","name":"copyright","label":"Copyright"}]}}