A Proper Generalized Decomposition for the solution of elliptic problems in abstract form by using a functional Eckart-Young approach

被引：52
作者：
Falco, A. [1 ]
Nouy, A. [2 ]
机构：
[1] Univ CEU Cardenal Herrera, Dept Ciencias Fis Matemat & Computac, Alfara Del Patriarca 46115, Valencia, Spain
[2] Univ Nantes, Ecole Cent Nantes, UMR CNRS 6183, GeM Inst Rech Genie Civil & Mecan, F-44321 Nantes 3, France
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2011年 / 376卷 / 02期
关键词：
Proper Generalized Decomposition; Singular values; Tensor product Hilbert spaces; SPECTRAL DECOMPOSITION; COMPUTATIONAL STRATEGY; APPROXIMATION; SOLVERS; FAMILY; CHAOS; TIME; RANK;
D O I：
10.1016/j.jmaa.2010.12.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The Proper Generalized Decomposition (PGD) is a methodology initially proposed for the solution of partial differential equations (PDE) defined in tensor product spaces. It consists in constructing a separated representation of the solution of a given PDE. In this paper we consider the mathematical analysis of this framework for a larger class of problems in an abstract setting. In particular, we introduce a generalization of Eckart and Young theorem which allows to prove the convergence of the so-called progressive PGD for a large class of linear problems defined in tensor product Hilbert spaces. (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：469 / 480
页数：12
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