Sign in
Author

Conference

Journal

Organization

Year

DOI
Look for results that meet for the following criteria:
since
equal to
before
between
and
Search in all fields of study
Limit my searches in the following fields of study
Agriculture Science
Arts & Humanities
Biology
Chemistry
Computer Science
Economics & Business
Engineering
Environmental Sciences
Geosciences
Material Science
Mathematics
Medicine
Physics
Social Science
Multidisciplinary
Keywords
(4)
Eigenvalue Problem
Eigenvalues
Elliptic Operator
Inverse Iteration
Related Publications
(2)
Adaptive eigenvalue computation: complexity estimates
A geometric theory for preconditioned inverse iteration III: A short and sharp convergence estimate for generalized eigenvalue problems
Subscribe
Academic
Publications
Perturbed preconditioned inverse iteration for operator eigenvalue problems with applications to adaptive wavelet discretization
Perturbed preconditioned inverse iteration for operator eigenvalue problems with applications to adaptive wavelet discretization,10.1007/s1044400991
Edit
Perturbed preconditioned inverse iteration for operator eigenvalue problems with applications to adaptive wavelet discretization
(
Citations: 2
)
BibTex

RIS

RefWorks
Download
Thorsten Rohwedder
,
Reinhold Schneider
,
Andreas Zeiser
In this paper we discuss an abstract iteration scheme for the calculation of the smallest eigenvalue of an
elliptic operator
eigenvalue problem. A short and geometric proof based on the preconditioned
inverse iteration
(PINVIT) for matrices [Knyazev and Neymeyr, (2009)] is extended to the case of operators. We show that convergence is retained up to any tolerance if one only uses approximate applications of operators which leads to the perturbed preconditioned
inverse iteration
(PPINVIT). We then analyze the Besov regularity of the eigenfunctions of the Poisson
eigenvalue problem
on a polygonal domain, showing the advantage of an adaptive solver to uniform refinement when using a stable wavelet base. A numerical example for PPINVIT, applied to the model problem on the Lshaped domain, is shown to reproduce the predicted behaviour.
Journal:
Advances in Computational Mathematics  Adv. Comput. Math.
, vol. 34, no. 1, pp. 4366, 2011
DOI:
10.1007/s1044400991418
Cumulative
Annual
View Publication
The following links allow you to view full publications. These links are maintained by other sources not affiliated with Microsoft Academic Search.
(
www.springerlink.com
)
(
www.springerlink.com
)
(
www.informatik.unitrier.de
)
(
dx.doi.org
)
(
arxiv.org
)
More »
Citation Context
(2)
...See also [
RSZ
] for further references and comments...
...While the first option  although with the same motivation as in the present work  has been adopted in [
RSZ
], we address here the algorithmic realization of the second option...
...In fact, in [
RSZ
], from a somewhat dierent perspective, we focus on convergence of preconditioned iteration schemes per se, whereas in the present paper we develop and...
...[KN,
RSZ
]. Note that the preconditioning is already provided through the formulation as a wellconditioned problem in ‘2(I)...
Wolfgang Dahmen
,
et al.
Adaptive eigenvalue computation: complexity estimates
...ditioner is chosen appropriately; in [
40
, 11], an adaptive variant was recently proposed...
Reinhold Schneider
,
et al.
Direct minimization for calculating invariant subspaces in density fun...
References
(37)
Adaptive Wavelet Schemes for Elliptic Problems  Implementation and Numerical Experiments
(
Citations: 32
)
Arne Barinka
,
Titus Barsch
,
Philippe Charton
,
Albert Cohen
,
Stephan Dahlke
,
Wolfgang Dahmen
,
Karsten Urban
Journal:
Siam Journal on Scientific Computing
, 1998
An optimal control approach to a posteriori error estimation in finite element methods
(
Citations: 243
)
Roland Becker
,
Rolf Rannacher
Journal:
Acta Numerica
, vol. 10, 2001
Fast wavelet transforms and numerical algorithms I
(
Citations: 780
)
G. Beylkin
,
R. Coifman
,
V. Rokhlin
Journal:
Communications on Pure and Applied Mathematics  COMMUN PURE APPL MATH
, vol. 44, no. 2, pp. 141183, 1991
Adaptive wavelet methods for elliptic operator equations: Convergence rates
(
Citations: 146
)
Albert Cohen
,
Wolfgang Dahmen
,
Ronald A. Devore
Journal:
Mathematics of Computation  Math. Comput.
, vol. 70, no. 233, pp. 2775, 2001
Adaptive frame methods for elliptic operator equations
(
Citations: 33
)
Stephan Dahlke
,
Massimo Fornasier
,
Thorsten Raasch
Journal:
Advances in Computational Mathematics  Adv. Comput. Math.
, vol. 27, no. 1, pp. 2763, 2007
Sort by:
Citations
(2)
Adaptive eigenvalue computation: complexity estimates
(
Citations: 7
)
Wolfgang Dahmen
,
Thorsten Rohwedder
,
Reinhold Schneider
,
Andreas Zeiser
Journal:
Numerische Mathematik  NUMER MATH
, vol. 110, no. 3, pp. 277312, 2008
Direct minimization for calculating invariant subspaces in density functional computations of the electronic structure
(
Citations: 6
)
Reinhold Schneider
,
Thorsten Rohwedder
,
Alexej Neelov
,
Johannes Blauert
Published in 2008.