scholarly journals Subspace Correction Methods for Total Variation and $\ell_1$-Minimization

2009 ◽  
Vol 47 (5) ◽  
pp. 3397-3428 ◽  
Author(s):  
Massimo Fornasier ◽  
Carola-Bibiane Schönlieb
Keyword(s):  
Total Variation ◽  
Subspace Correction ◽  
Subspace Correction Methods

scholarly journals Subspace correction methods for nonsymmetric parabolic problems

2001 ◽  
Vol 332-334 ◽  
pp. 205-234 ◽  
Author(s):  
Øystein Rognes ◽  
Xue-Cheng Tai
Keyword(s):  
Parabolic Problems ◽  
Subspace Correction ◽  
Subspace Correction Methods

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.

scholarly journals Stochastic subspace correction methods and fault tolerance

2019 ◽  
Vol 89 (321) ◽  
pp. 279-312
Author(s):  
Michael Griebel ◽  
Peter Oswald
Keyword(s):  
Fault Tolerance ◽  
Subspace Correction ◽  
Subspace Correction Methods

scholarly journals Subspace correction methods in algebraic multi-level frames

2016 ◽  
Vol 488 ◽  
pp. 505-521
Author(s):  
Peter Zaspel
Keyword(s):  
Subspace Correction ◽  
Subspace Correction Methods ◽  
Multi Level
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