000190659 001__ 190659
000190659 005__ 20190316235746.0
000190659 0247_ $$2doi$$a10.1051/m2an/2013100
000190659 022__ $$a0764-583X
000190659 037__ $$aARTICLE
000190659 245__ $$aEfficient greedy algorithms for high-dimensional parameter spaces with applications to empirical interpolation and reduced basis methods
000190659 269__ $$a2014
000190659 260__ $$bEDP Sciences$$c2014
000190659 336__ $$aJournal Articles
000190659 520__ $$aWe propose two new and enhanced algorithms for greedy sampling of high- dimensional functions. While the techniques have a substantial degree of generality, we frame the discussion in the context of methods for empirical interpolation and the devel- opment of reduced basis techniques for high-dimensional parametrized functions. The first algorithm, based on a assumption of saturation of error in the greedy algorithm, is shown to result in a significant reduction of the workload over the standard greedy algorithm. In an improved approach, this is combined with an algorithm in which the train set for the greedy approach is adaptively sparsefied and enriched. A safety check step is added at the end of the algorithm to certify the quality of the basis set. Both these techniques are applicable to high-dimensional problems and we shall demonstrate their performance on a number of numerical examples.
000190659 700__ $$0247428$$g232231$$aHesthaven, Jan S.
000190659 700__ $$aStamm, Benjamin
000190659 700__ $$aZhang, Shun
000190659 773__ $$j48$$tMathematical Modelling and Numerical Analysis$$k01$$q259-283
000190659 8564_ $$uhttps://infoscience.epfl.ch/record/190659/files/M2AN482014.pdf$$zPublisher's version$$s1186212$$yPublisher's version
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000190659 937__ $$aEPFL-ARTICLE-190659
000190659 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000190659 980__ $$aARTICLE