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Títol:
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Algebraic PGD for tensor separation and compression: an algorithmic approach
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Autor/a:
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Díez, Pedro; Zlotnik, Sergio; García González, Alberto; Huerta, Antonio
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Altres autors:
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Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental; Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria |
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Abstract:
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Proper Generalized Decomposition (PGD) is devised as a computational method to solve high-dimensional boundary value problems (where many dimensions are associated with the space of parameters defining the problem). The PGD philosophy consists in providing a separated representation of the multidimensional solution using a greedy approach combined with an alternated directions scheme to obtain the successive rank-one terms. This paper presents an algorithmic approach to high-dimensional tensor separation based on solving the Least Squares approximation in a separable format of multidimensional tensor using PGD. This strategy is usually embedded in a standard PGD code in order to compress the solution (reduce the number of terms and optimize the available storage capacity), but it stands also as an alternative and highly competitive method for tensor separation. |
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Abstract:
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Peer Reviewed |
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Matèries:
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
-System theory
-Tensor separation
-Algebraic PGD
-Least-squares approximation
-Sistemes de control
-Classificació AMS::93 Systems Theory; Control::93B Controllability, observability, and system structure |
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Drets:
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Tipus de document:
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Article - Versió presentada
Article |
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