{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T07:47:08Z","timestamp":1758268028267},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2012,6,19]],"date-time":"2012-06-19T00:00:00Z","timestamp":1340064000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Found Comput Math"],"published-print":{"date-parts":[[2013,10]]},"DOI":"10.1007\/s10208-012-9125-9","type":"journal-article","created":{"date-parts":[[2012,6,18]],"date-time":"2012-06-18T18:39:07Z","timestamp":1340044747000},"page":"763-787","source":"Crossref","is-referenced-by-count":9,"title":["Approximation of Parametric Derivatives by the Empirical Interpolation Method"],"prefix":"10.1007","volume":"13","author":[{"given":"Jens L.","family":"Eftang","sequence":"first","affiliation":[]},{"given":"Martin A.","family":"Grepl","sequence":"additional","affiliation":[]},{"given":"Anthony T.","family":"Patera","sequence":"additional","affiliation":[]},{"given":"Einar M.","family":"R\u00f8nquist","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,6,19]]},"reference":[{"key":"9125_CR1","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1016\/j.crma.2004.08.006","volume":"339","author":"M. Barrault","year":"2004","unstructured":"M. Barrault, N.C. Nguyen, Y. Maday, A.T. Patera, An \u201cempirical interpolation\u201d method: application to efficient reduced-basis discretization of partial differential equations, C. R. Math. 339, 667\u2013672 (2004).","journal-title":"C. R. Math."},{"key":"9125_CR2","first-page":"209","volume-title":"Handbook of Numerical Analysis","author":"C. Bernardi","year":"1997","unstructured":"C. Bernardi, Y. Maday, Spectral methods, in Handbook of Numerical Analysis (North-Holland, Amsterdam, 1997), pp. 209\u2013485."},{"issue":"2","key":"9125_CR3","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1006\/jcph.1997.5743","volume":"136","author":"J. Borggaard","year":"1997","unstructured":"J. Borggaard, J. Burns, A PDE sensitivity equation method for optimal aerodynamic design, J. Comput. Phys. 136(2), 366\u2013384 (1997).","journal-title":"J. Comput. Phys."},{"key":"9125_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-30726-6","volume-title":"Spectral methods. Scientific Computation","author":"C. Canuto","year":"2006","unstructured":"C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral methods. Scientific Computation, (Springer, Berlin, 2006)."},{"key":"9125_CR5","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/BF02124750","volume":"5","author":"R. Corless","year":"1996","unstructured":"R. Corless, G. Gonnet, D. Hare, D. Jeffrey, D. Knuth, On the Lambert W function, Adv. Comput. Math. 5, 329\u2013359 (1996).","journal-title":"Adv. Comput. Math."},{"issue":"9\u201310","key":"9125_CR6","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1016\/j.crma.2010.03.004","volume":"348","author":"J.L. Eftang","year":"2010","unstructured":"J.L. Eftang, M.A. Grepl, A.T. Patera, A posteriori error bounds for the empirical interpolation method, C. R. Math. 348(9\u201310), 575\u2013579 (2010).","journal-title":"C. R. Math."},{"key":"9125_CR7","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1142\/S0218202511500151","volume":"22","author":"M. Grepl","year":"2012","unstructured":"M. Grepl, A posteriori error bounds for reduced-basis approximations of nonaffine and nonlinear parabolic partial differential equations, Math. Models Methods Appl. Sci. 22, 3 (2012).","journal-title":"Math. Models Methods Appl. Sci."},{"issue":"3","key":"9125_CR8","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1051\/m2an:2007031","volume":"41","author":"M.A. Grepl","year":"2007","unstructured":"M.A. Grepl, Y. Maday, N.C. Nguyen, A.T. Patera, Efficient reduced basis treatment of nonaffine and nonlinear partial differential equations, ESAIM: M2AN 41(3), 575\u2013605 (2007).","journal-title":"ESAIM: M2AN"},{"key":"9125_CR9","first-page":"383","volume":"8","author":"Y. Maday","year":"2009","unstructured":"Y. Maday, N.C. Nguyen, A.T. Patera, G.S.H. Pau, A general multipurpose interpolation procedure: the magic points, Commun. Pure Appl. Math. 8, 383\u2013404 (2009).","journal-title":"Commun. Pure Appl. Math."},{"key":"9125_CR10","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/s11081-007-9002-6","volume":"8","author":"I. Oliveira","year":"2007","unstructured":"I. Oliveira, A. Patera, Reduced-basis techniques for rapid reliable optimization of systems described by affinely parametrized coercive elliptic partial differential equations, Optim. Eng. 8, 43\u201365 (2007).","journal-title":"Optim. Eng."},{"key":"9125_CR11","series-title":"Texts Appl. Math.","volume-title":"Numerical Mathematics","author":"A. Quarteroni","year":"1991","unstructured":"A. Quarteroni, R. Sacco, F. Saleri, Numerical Mathematics. Texts Appl. Math., vol.\u00a037 (Springer, New York, 1991)."},{"issue":"5","key":"9125_CR12","doi-asserted-by":"crossref","first-page":"2176","DOI":"10.1137\/040603280","volume":"42","author":"S.C. Reddy","year":"2005","unstructured":"S.C. Reddy, J.A.C. Weideman, The accuracy of the Chebyshev differencing method for analytic functions, SIAM J. Numer. Anal. 42(5), 2176\u20132187 (2005).","journal-title":"SIAM J. Numer. Anal."},{"key":"9125_CR13","volume-title":"The Chebyshev Polynomials","author":"T.J. Rivlin","year":"1974","unstructured":"T.J. Rivlin, The Chebyshev Polynomials (Wiley-Interscience, New York, 1974)."},{"issue":"3","key":"9125_CR14","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/s11831-008-9019-9","volume":"15","author":"G. Rozza","year":"2008","unstructured":"G. Rozza, D.B.P. Huynh, A.T. Patera, Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations, Arch. Comput. Methods Eng. 15(3), 229\u2013275 (2008).","journal-title":"Arch. Comput. Methods Eng."},{"issue":"1","key":"9125_CR15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/0723001","volume":"23","author":"E. Tadmor","year":"1986","unstructured":"E. Tadmor, The exponential accuracy of Fourier and Chebyshev differencing methods, SIAM J. Numer. Anal. 23(1), 1\u201310 (1986).","journal-title":"SIAM J. Numer. Anal."}],"container-title":["Foundations of Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-012-9125-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10208-012-9125-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-012-9125-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,30]],"date-time":"2019-06-30T02:56:29Z","timestamp":1561863389000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10208-012-9125-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,19]]},"references-count":15,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2013,10]]}},"alternative-id":["9125"],"URL":"https:\/\/doi.org\/10.1007\/s10208-012-9125-9","relation":{},"ISSN":["1615-3375","1615-3383"],"issn-type":[{"value":"1615-3375","type":"print"},{"value":"1615-3383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6,19]]}}}