A general multipurpose interpolation procedure: the magic points

By Yvon Maday, Ngoc Cuong Nguyen, Anthony T. Patera, George Shu Heng Pau. 2008

308 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f27843d643d9684a6925752135b6e5a0054e6040

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In Computational Theory and Mathematics

In Statistical and Nonlinear Physics

In Statistics and Probability

Citations in the corpus

Surrogate model of hybridized numerical relativity binary black hole waveforms (2018, methodology): “Next, using a different greedy procedure, we construct an empirical interpolant [101–103] in time.”
The Generalized Empirical Interpolation Method: Stability theory on Hilbert spaces with an application to the Stokes equation (2015, background): “Although several procedures have been explored in this direction (we refer to [4], [5] and also to the kriging studies in the stochastic community such as [6]), of particular interest for the present work is the Empirical Interpolation Method (EIM, [2], [7], [8]) that has been developed in the broad”
Model Order Reduction in Fluid Dynamics: Challenges and Perspectives (2014, unknown): “[15, 85].”
Adaptive reduced basis finite element heterogeneous multiscale method (2013, background): “Details of the EIM can be found in [30, 31].”
Surrogate models for precessing binary black hole simulations with unequal masses (2019, methodology): “We then construct an empirical time interpolant with the same number of empirical time nodes as basis functions for that data piece [92–94].”
A ‘best points’ interpolation method for efficient approximation of parametrized functions (2008, background): “[15–17] introduced the empirical interpolation method (EIM) that also deals with the interpolation of parametrized functions.”
The Empirical Interpolation Method (2013, methodology): “In [15] EIM was generalized to use generic approximation spaces rather than to approximate a single parametrized function f(x;μ).”
Low-rank methods for high-dimensional approximation and model order reduction (2015, unknown): “n Πǫ(w) of a tensor w such that kw − Πǫ(w)k∞≤ ǫkwk∞, where kwk∞= maxi1,...,iD |wi1,...,iD|. A practical implementation of the truncation operator Πǫ can be based on the Empirical Interpolation Method [5, 58] or higherorder extensions of Adaptive Cross Approximation (ACA) algorithms [72]. Remark 7.1 ”
High-performance model reduction techniques in computational multiscale homogenization (2014, unknown): “[46].”
The Future of Sensitivity Analysis: An essential discipline for systems modeling and policy support (2020, unknown): “Greedy sampling methods can be used to reduce the computational cost of optimization-based sampling methods (Oakley and O ’ Hagan, 2004; Maday et al., 2009; Schaback and Wendlend 2006; Jakeman et al., 2019; Harbrecht et al., 2020), but while being efficient in many cases, they can still ultimately…”