Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10637/11648
Título : On the Dirac-Frenkel variational principle on tensor banach spaces
Autor : Falcó Montesinos, Antonio.
Hackbusch, Wolfgang.
Nouy, Anthony.
Materias: Banach spaces.Espacios generalizados.Generalized spaces.Calculus of tensors.Geometry, Differential.Banach, Espacios de.Cálculo tensorial.Geometría diferencial.
Fecha de publicación : 1-feb-2019
Editorial : Springer Nature.
Citación : Falcó, A., Hackbusch, W. & Nouy, A. (2019). On the Dirac-Frenkel variational principle on tensor banach spaces. Foundations of Computational Mathematics, vol. 19, n. 1 (feb.), pp. 159-204. DOI: https://doi.org/10.1007/s10208-018-9381-4
Resumen : The main goal of this paper is to extend the so-called Dirac-Frenkel Variational Principle in the framework of tensor Banach spaces. To this end we observe that a tensor product of normed spaces can be described as a union of disjoint connected components. Then we show that each of these connected components, composed by tensors in Tucker format with a fixed rank, is a Banach manifold modelled in a particular Banach space, for which we provide local charts. The description of the local charts of these manifolds is crucial for an algorithmic treatment of high-dimensional partial differential equations and minimization problems. In order to describe the relationship between these manifolds and the natural ambient space we prove under natural conditions that each connected component can be immersed in a particular ambient Banach space. This fact allows us to finally extend the Dirac-Frenkel variational principle in the framework of topological tensor spaces.
Descripción : Este artículo se encuentra disponible en la página web de la revista en la siguiente URL: https://link.springer.com/article/10.1007/s10208-018-9381-4
Este documento se encuentra disponible en: https://arxiv.org/pdf/1610.09865.pdf
Este es el pre-print del siguiente artículo Falcó, A., Hackbusch, W. & Nouy, A. (2019). On the Dirac-Frenkel variational principle on tensor banach spaces. Foundations of Computational Mathematics, vol. 19, n. 1 (feb.), pp. 159-204, que se ha publicado de forma definitiva en https://doi.org/10.1007/s10208-018-9381-4
This is the pre-peer reviewed version of the following article: Falcó, A., Hackbusch, W. & Nouy, A. (2019). On the Dirac-Frenkel variational principle on tensor banach spaces. Foundations of Computational Mathematics, vol. 19, n. 1 (feb.), pp. 159-204, which has been published in final form at https://doi.org/10.1007/s10208-018-9381-4
URI : http://hdl.handle.net/10637/11648
Derechos: http://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
ISSN : 1615-3375
1615-3383 (Electrónico)
Aparece en las colecciones: Dpto. Matemáticas, Física y Ciencias Tecnológicas

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