{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,27]],"date-time":"2024-08-27T08:30:16Z","timestamp":1724747416904},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2015,2,18]],"date-time":"2015-02-18T00:00:00Z","timestamp":1424217600000},"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":["Adv Comput Math"],"published-print":{"date-parts":[[2015,10]]},"DOI":"10.1007\/s10444-015-9410-7","type":"journal-article","created":{"date-parts":[[2015,2,17]],"date-time":"2015-02-17T22:46:13Z","timestamp":1424213173000},"page":"1231-1253","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Parametric model order reduction with a small \u210b 2 $\\mathcal {H}_{2}$ -error using radial basis functions"],"prefix":"10.1007","volume":"41","author":[{"given":"Peter","family":"Benner","sequence":"first","affiliation":[]},{"given":"Sara","family":"Grundel","sequence":"additional","affiliation":[]},{"given":"Nils","family":"Hornung","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,2,18]]},"reference":[{"issue":"7","key":"9410_CR1","doi-asserted-by":"crossref","first-page":"1803","DOI":"10.2514\/1.35374","volume":"46","author":"D Amsallem","year":"2008","unstructured":"Amsallem, D., Farhat, C.: Interpolation method for adapting reduced-order models and application to aeroelasticity. AIAA J. 46(7), 1803\u20131813 (2008)","journal-title":"AIAA J."},{"issue":"8","key":"9410_CR2","doi-asserted-by":"crossref","first-page":"2889","DOI":"10.1016\/j.laa.2011.07.017","volume":"436","author":"A Antoulas","year":"2012","unstructured":"Antoulas, A., Ionita, A, Lefteriu, S: On two-variable rational interpolation. Linear Algebra Appl. 436(8), 2889\u20132915 (2012)","journal-title":"Linear Algebra Appl."},{"issue":"3","key":"9410_CR3","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1090\/S0002-9947-1950-0051437-7","volume":"68","author":"N Aronszajn","year":"1950","unstructured":"Aronszajn, N.: Theory of reproducing kernels. Trans. Amer. Math .Soc. 68(3), 337\u2013404 (1950). doi: 10.1090\/S0002-9947-1950-0051437-7","journal-title":"Trans. Amer. Math .Soc."},{"issue":"5","key":"9410_CR4","doi-asserted-by":"crossref","first-page":"2489","DOI":"10.1137\/090776925","volume":"33","author":"U Baur","year":"2011","unstructured":"Baur, U., Beattie, C.A., Benner, P., Gugercin, S.: Interpolatory projection methods for parameterized model reduction. SIAM J. Sci. Comput. 33(5), 2489\u20132518 (2011a)","journal-title":"SIAM J. Sci. Comput."},{"issue":"4","key":"9410_CR5","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1080\/13873954.2011.547658","volume":"17","author":"U Baur","year":"2011","unstructured":"Baur, U., Benner, P., Greiner, A., Korvink, J., Lienemann, J., Moosmann, C.: Parameter preserving model order reduction for mems applications. Math. Comp. Model. Dyn. 17(4), 297\u2013317 (2011b). doi: 10.1080\/13873954.2011.547658","journal-title":"Math. Comp. Model. Dyn."},{"issue":"9","key":"9410_CR6","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1002\/nla.622","volume":"15","author":"P Benner","year":"2008","unstructured":"Benner, P., Li, J.R., Penzl, T.: Numerical solution of large-scale Lyapunov equations, Riccati equations, and linear-quadratic optimal control problems. Numer. Lin. Alg. Appl. 15(9), 755\u2013777 (2008)","journal-title":"Numer. Lin. Alg. Appl."},{"key":"9410_CR7","unstructured":"Benner, P., Gugercin, S., Willcox, K.: A survey of model reduction methods for parametric systems. Max Planck Institute Magdeburg Preprint MPIMD\/13-14, available from http:\/\/www.mpi-magdeburg.mpg.de\/preprints\/ (2013)"},{"key":"9410_CR8","doi-asserted-by":"crossref","unstructured":"Benner, P., Grundel, S., Hornung, N.: Parametric Model Order Reduction with Small \u210b 2 $\\mathcal {H}_{2}$ -Error Using Radial Basis Functions. Max Planck Institute Magdeburg Preprint MPIMD\/14-01, available from http:\/\/www.mpi-magdeburg.mpg.de\/preprints\/ (2014)","DOI":"10.1007\/s10444-015-9410-7"},{"issue":"2","key":"9410_CR9","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/BF01061480","volume":"2","author":"JP Boyd","year":"1987","unstructured":"Boyd, J.P.: Exponentially convergent Fourier-Chebshev quadrature schemes on bounded and infinite intervals. J. Sci. Comput. 2(2), 99\u2013109 (1987). doi 10.1007\/BF01061480","journal-title":"J. Sci. Comput."},{"issue":"5","key":"9410_CR10","doi-asserted-by":"crossref","first-page":"1202","DOI":"10.1016\/j.cam.2008.12.029","volume":"233","author":"A Bunse-Gerstner","year":"2010","unstructured":"Bunse-Gerstner, A., Kubali\u0144ska, D., Vossen, G., Wilczek, D.: h 2-norm optimal model reduction for large scale discrete dynamical MIMO systems. J. Comput. Appl. Math. 233(5), 1202\u20131216 (2010). doi 10.1016\/j.cam.2008.12.029","journal-title":"J. Comput. Appl. Math."},{"key":"9410_CR11","doi-asserted-by":"crossref","unstructured":"Fasshauer, G.E.: Meshfree Approximation Methods with MATLAB (with CD-ROM). World Scientific (2007)","DOI":"10.1142\/6437"},{"key":"9410_CR12","volume-title":"Dissertation","author":"EJ Grimme","year":"1997","unstructured":"Grimme, E.J.: Krylov projection methods for model reduction Dissertation. University of Illinois at Urbana-Champaign, USA (1997)"},{"issue":"2","key":"9410_CR13","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1137\/060666123","volume":"30","author":"S Gugercin","year":"2008","unstructured":"Gugercin, S., Antoulas, A.C., Beattie, C.: \u210b 2 $\\mathcal {H}_{2}$ Model Reduction for Large-Scale Linear Dynamical Systems. SIAM. J. Matrix Anal. Appl. 30(2), 609\u2013638 (2008)","journal-title":"SIAM. J. Matrix Anal. Appl."},{"issue":"5","key":"9410_CR14","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1109\/TAC.1967.1098680","volume":"12","author":"IL Meier","year":"1967","unstructured":"Meier, I.L., Luenberger, D.: Approximation of linear constant systems. IEEE Trans. Automat. Control 12(5), 585\u2013588 (1967). doi: 10.1109\/TAC.1967.1098680","journal-title":"IEEE Trans. Automat. Control"},{"key":"9410_CR15","unstructured":"Moosmann, C., Rudnyi, E., Greiner, A., Korvink, J., Hornung, M: Parameter preserving model order reduction of a flow meter. Tech. Proc. Nanotech 2005 (2005)"},{"key":"9410_CR16","unstructured":"Panzer, H., Hubele, J., Eid, R, Lohmann, B.: Generating a parametric finite element model of a 3D cantilever Timoshenko beam using MATLAB. Technical reports on automatic control, available from https:\/\/mediatum.ub.tum.de (2009)"},{"issue":"8","key":"9410_CR17","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1524\/auto.2010.0863","volume":"58","author":"H Panzer","year":"2010","unstructured":"Panzer, H., Mohring, J., Eid, R., Lohmann, B.: Parametric model order reduction by matrix interpolation. at-Automatisierungstechnik 58(8), 475\u2013484 (2010)","journal-title":"at-Automatisierungstechnik"},{"key":"9410_CR18","doi-asserted-by":"crossref","unstructured":"Rieger, C, Schaback, R, Zwicknagl, B: Sampling and stability. In: D\u00e6hlen, M., Floater, M., Lyche, T, Merrien, J.L., M\u00f8rken, K., Schumaker, L.L. (eds.) Mathematical Methods for Curves and Surfaces, Lect. Notes Comput. Sc., vol. 5862, pp. 347\u2013369 . Springer, Berlin Heidelberg (2010), doi: 10.1007\/978-3-642-11620-9_23","DOI":"10.1007\/978-3-642-11620-9_23"},{"key":"9410_CR19","doi-asserted-by":"crossref","unstructured":"Schaback, R.: Native Hilbert spaces for radial basis functions I. In: M\u00fcller, M.W., Buhmann, M.D., Mache, D.H., Felten, M. (eds.) New Developments in Approximation Theory, ISNM Internat. Ser. Numer. Math., vol 132, Birkh\u00e4user Basel, pp 255\u2013282 (1999), doi: 10.1007\/978-3-0348-8696-3_16","DOI":"10.1007\/978-3-0348-8696-3_16"},{"key":"9410_CR20","doi-asserted-by":"crossref","unstructured":"Positive definite functions and generalizations, an historical survey. Rocky Mountain J. Math. 6(3), 409\u2013434 (1976). doi: 10.1216\/RMJ-1976-6-3-409","DOI":"10.1216\/RMJ-1976-6-3-409"},{"issue":"12","key":"9410_CR21","doi-asserted-by":"crossref","first-page":"1267","DOI":"10.1016\/j.aml.2007.09.015","volume":"21","author":"P Van Dooren","year":"2008","unstructured":"Van Dooren, P., Gallivan, K.A., Absil, P.-A.: \u210b 2 $\\mathcal {H}_{2}$ -optimal model reduction of MIMO systems. Appl. Math. Lett. 21(12), 1267\u20131273 (2008). doi: 10.1016\/j.aml.2007.09.015","journal-title":"Appl. Math. Lett."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-015-9410-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-015-9410-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-015-9410-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,21]],"date-time":"2019-08-21T01:08:55Z","timestamp":1566349735000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-015-9410-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,18]]},"references-count":21,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2015,10]]}},"alternative-id":["9410"],"URL":"https:\/\/doi.org\/10.1007\/s10444-015-9410-7","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2,18]]}}}