On the Convergence of a Greedy Rank-One Update Algorithm for a Class of Linear Systems

被引：64

作者：

Ammar, A. ^{[1
]}

Chinesta, F. ^{[2
]}

Falco, A. ^{[3
]}

机构：

[1] Arts & Metiers Paris Tech, F-49035 Angers 01, France

[2] Ecole Cent Nantes, Inst Rech Genie Civil & Mecan GeM, F-44321 Nantes 3, France

[3] Univ CEU Cardenal Herrera, Dept Ciencias Fis Matemat & Computac, Valencia 46115, Spain

来源：

ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING | 2010年 / 17卷 / 04期

关键词：

APPROXIMATION; SOLVERS; FAMILY;

D O I：

10.1007/s11831-010-9048-z

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this paper we study the convergence of the well-known Greedy Rank-One Update Algorithm. It is used to construct the rank-one series solution for full-rank linear systems. The existence of the rank one approximations is also not new, but surprisingly the focus there has been more on the applications side more that in the convergence analysis. Our main contribution is to prove the convergence of the algorithm and also we study the required rank one approximation in each step. We also give some numerical examples and describe its relationship with the Finite Element Method for High-Dimensional Partial Differential Equations based on the tensorial product of one-dimensional bases. We illustrate this situation taking as a model problem the multidimensional Poisson equation with homogeneous Dirichlet boundary condition.

引用

页码：473 / 486

页数：14

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