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龚禾林1, 张世全2, Yvon Maday3
龚禾林, 张世全, Yvon Maday. EIM魔数点特性研究及其最小二乘格式[J]. 数值计算与计算机应用, 2023, 44(1): 25-36.
Gong Helin, Zhang Shiquan, Yvon Maday. THE OPTIMUM OF EIM MAGIC POINTS AND THE LEAST-SQUARES FORM[J]. Journal on Numerica Methods and Computer Applications, 2023, 44(1): 25-36.
Gong Helin1, Zhang Shiquan2, Yvon Maday3
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[1] Barrault M, Maday Y, Nguyen N C, Patera AT. An ‘empirical interpolation’ method:application to efficient reduced-basis discretization of partial differential equations[J]. Comptes Rendus Mathematique, 2004, 339(9):667-672. [2] Grepl M A, Maday Y, Nguyen N C, Patera A T. Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations[J]. ESAIM:Mathematical Modelling and Numerical Analysis, 2007, 41(3):575-605. [3] Maday Y, Nguyen N C, Patera A T, Pau S H. A general multipurpose interpolation procedure:the magic points[J]. Communications on Pure & Applied Analysis, 2009, 8(1):383-404. [4] Maday Y, Patera A T, Turinici G. A priori convergence theory for reduced-basis approximations of single-parameter elliptic partial differential equations[J]. Journal of Scientific Computing, 2002, 17(1-4):437-446. [5] Maday Y. Reduced basis method for the rapid and reliable solution of partial differential equations[C]. In International Congress of Mathematicians, Eur. Math. Soc. Zurich. Citeseer. 2006, III:1255-1270. [6] Rozza G, Huynh D B P, Patera A T. Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations[J]. Archives of Computational Methods in Engineering, 2008, 15(3):229-275. [7] Maday Y, Mula O, Turinici G. Convergence analysis of the generalized empirical interpolation method[J]. SIAM Journal on Numerical Analysis, 2016, 54(3):1713-1731. [8] Argaud J P, Bouriquet B, De Caso F, Gong H, Maday Y, Mula O. Sensor placement in nuclear reactors based on the generalized empirical interpolation method[J]. Journal of Computational Physics, 2018, 363:354-370. [9] Gong H, Argaud J P, Bouriquet B, Maday Y. The Empirical Interpolation Method applied to the neutron diffusion equations with parameter dependence[C]. In Proceedings of PHYSOR. 2016. [10] Argaud J P, Bouriquet B, Gong H, Maday Y, Mula O. Stabilization of (G) EIM in presence of measurement noise:application to nuclear reactor physics[C]. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016. Springer, Cham, 2017. 133-145. [11] Ghavamian F, Tiso P, Simone A. POD-DEIM model order reduction for strain-softening viscoplasticity[J]. Computer Methods in Applied Mechanics and Engineering, 2017, 317:458-79. [12] Zhou Y B. Model Reduction for Nonlinear Dynamical Systems with Parametric Uncertainties[D]. Massachusetts Institute of Technology, 2012. [13] Everson R, Sirovich L. Karhunen-Loeve procedure for gappy data[J]. Journal of the Optical Society of America A, 1995, 12(8):1657-1664. [14] Willcox K E. Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition[J]. Computers & fluids, 2006, 35(2):208-226. [15] Bebendorf M, Maday Y, Stamm B. Comparison of some reduced representation approximations. In Reduced Order Methods for Modeling and Computational Reduction[B]. Springer, 2014, 67-100. [16] Cohen A, Davenport M A, Leviatan D. On the stability and accuracy of least squares approximations[J]. Foundations of computational mathematics, 2013, 13(5):819-834. [17] Cohen A, Migliorati G. Optimal weighted least-squares methods[J]. The SMAI journal of computational mathematics, 2017, 3:181-203. [18] Nevai P, Freud G. Orthogonal polynomials and Christoffel functions:A case study[J]. Journal of Approximation Theory, 1986, 48(1):3-167. |
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