TR32-Database: Database of Transregio 32

[789] - Optimized wavelet preconditioning

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Features
Citation
Kunoth, A., 2009. Optimized wavelet preconditioning. In: DeVore, R.A. and Kunoth, A. (Eds.): Multiscale, Nonlinear and Adaptive Approximation. Springer, Heidelberg, 325 - 378. DOI: 10.1007/978-3-642-03413-8_10.
Identification
Title(s):Main Title: Optimized wavelet preconditioning
Description(s):Abstract: The numerical solution of linear stationary variational problems involving elliptic partial differential operators usually requires iterative solvers on account of their problem size. Our guiding principle is to devise theoretically and practically efficient iterative solution schemes which are optimal in the number of arithmetic operations, i.e., of linear complexity in the total number of unknowns. For these algorithms, asymptotically optimal preconditioners are indispensable. This article collects the main ingredients for multilevel preconditioners based on wavelets for certain systems of elliptic PDEs with smooth solutions. Specifically, we consider problems from optimal control with distributed or Dirichlet boundary control constrained by elliptic PDEs. Moreover, the wavelet characterization of function space norms will also be used in modelling the control functional, thereby extending the range of applicability over conventional methods. The wavelet preconditioners are optimized for these PDE systems to exhibit small absolute condition numbers and consequently entail absolute low iteration numbers, as numerical experiments show.
Identifier(s):DOI: 10.1007/978-3-642-03413-8_10
Responsible Party
Creator(s):Author: Angela Kunoth
Publisher:Springer
Topic
TR32 Topic:Other
Related Sub-project(s):C1, C7
Subject(s):CRC/TR32 Keywords: Wavelet
File Details
File Name:2009_Kunoth_Optimized_wavelet_preconditioning.pdf
Data Type:Text
Size(s):54 Pages
File Size:1662 kB (1.623 MB)
Date(s):Issued: 2009-09-05
Mime Type:application/pdf
Data Format:PDF
Language:English
Status:Completed
Constraints
Download Permission:OnlyTR32
General Access and Use Conditions:For internal use only
Access Limitations:For internal use only
Licence:TR32DB Data policy agreement
Geographic
North:-no map data
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Measurement Region:None
Measurement Location:--None--
Specific Informations - Publication
Status:Published
Review:PeerReview
Year:2009
Type:Book Section
Book Title:Multiscale, Nonlinear and Adaptive Approximation
Book Editor:DeVore, R.A. and Kunoth, A.
City:Heidelberg
Number Of Pages:54
Page Range:325 - 378
Metadata Details
Metadata Creator:Angela Kunoth
Metadata Created:2013-12-09
Metadata Last Updated:2015-05-07
Subproject:C1
Funding Phase:1
Metadata Language:English
Metadata Version:V41
Dataset Metrics
Page Visits:133
Metadata Downloads:0
Dataset Downloads:0
Dataset Activity
Features