scholarly journals Fast Eigenpairs Computation with Operator Adapted Wavelets and Hierarchical Subspace Correction

2019 ◽  
Vol 57 (6) ◽  
pp. 2519-2550 ◽  
Author(s):  
Hehu Xie ◽  
Lei Zhang ◽  
Houman Owhadi
Keyword(s):  
Subspace Correction

scholarly journals Automatic mapping operator construction for subspace correction method to solve a series of linear systems

JSIAM Letters ◽  
2017 ◽  
Vol 9 (0) ◽  
pp. 25-28 ◽  
Author(s):  
Takeshi Iwashita ◽  
Shigeru Kawaguchi ◽  
Takeshi Mifune ◽  
Tetsuji Matsuo
Keyword(s):  
Linear Systems ◽  
Correction Method ◽  
Subspace Correction ◽  
Automatic Mapping ◽  
Operator Construction

Low-Rank Tensor Methods with Subspace Correction for Symmetric Eigenvalue Problems

2014 ◽  
Vol 36 (5) ◽  
pp. A2346-A2368 ◽  
Author(s):  
Daniel Kressner ◽  
Michael Steinlechner ◽  
André Uschmajew
Keyword(s):  
Eigenvalue Problems ◽  
Low Rank ◽  
Tensor Methods ◽  
Rank Tensor ◽  
Subspace Correction ◽  
Symmetric Eigenvalue Problems

ROBUST SUBSPACE CORRECTION METHODS FOR NEARLY SINGULAR SYSTEMS

2007 ◽  
Vol 17 (11) ◽  
pp. 1937-1963 ◽  
Author(s):  
YOUNG-JU LEE ◽  
JINBIAO WU ◽  
JINCHAO XU ◽  
LUDMIL ZIKATANOV
Keyword(s):  
Singular Systems ◽  
Mesh Size ◽  
Singular Part ◽  
Multilevel Method ◽  
Subspace Correction ◽  
Convergence Results ◽  
Subspace Correction Methods ◽  
The Neumann Problem ◽  
Second Order Elliptic Problems ◽  
Element Discretizations

In this paper, we discuss convergence results for general (successive) subspace correction methods for solving nearly singular systems of equations. We provide parameter independent estimates under appropriate assumptions on the subspace solvers and space decompositions. The main assumption is that any component in the kernel of the singular part of the system can be decomposed into a sum of local (in each subspace) kernel components. This assumption also covers the case of "hidden" nearly singular behavior due to decreasing mesh size in the systems resulting from finite element discretizations of second order elliptic problems. To illustrate our abstract convergence framework, we analyze a multilevel method for the Neumann problem (H(grad) system), and also two-level methods for H(div) and H(curl) systems.

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