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Greedy Algorithms for High-Dimensional Eigenvalue Problems

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Abstract

In this article, we present two new greedy algorithms for the computation of the lowest eigenvalue (and an associated eigenvector) of a high-dimensional eigenvalue problem and prove some convergence results for these algorithms and their orthogonalized versions. The performance of our algorithms is illustrated on numerical test cases (including the computation of the buckling modes of a microstructured plate) and compared with that of another greedy algorithm for eigenvalue problems introduced by Ammar and Chinesta.

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Acknowledgments

This work has been done while E.C. and V.E. were long-term visitors at IPAM (UCLA). The authors would like to thank Sergey Dolgov, Venera Khoromskaia, and Boris Khoromskij for interesting discussions.

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Correspondence to Virginie Ehrlacher.

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Communicated by Vladimir N. Temlyakov.

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Cancès, E., Ehrlacher, V. & Lelièvre, T. Greedy Algorithms for High-Dimensional Eigenvalue Problems. Constr Approx 40, 387–423 (2014). https://doi.org/10.1007/s00365-014-9266-y

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  • DOI: https://doi.org/10.1007/s00365-014-9266-y

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