A Multilevel Method for Solving Operator Equations

We develop a multilevel method suitable for solving operator equations. This method combines the multiresolution structure of the spaces used to solve the operator equation with a Gauss–Seidel strategy to solve the associated matrix equations. We prove that this multilevel scheme has an optimal orde...

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Veröffentlicht in:Journal of mathematical analysis and applications 2001-10, Vol.262 (2), p.688-699
Hauptverfasser: Chen, Zhongying, Micchelli, Charles A., Xu, Yuesheng
Format: Artikel
Sprache:eng
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Zusammenfassung:We develop a multilevel method suitable for solving operator equations. This method combines the multiresolution structure of the spaces used to solve the operator equation with a Gauss–Seidel strategy to solve the associated matrix equations. We prove that this multilevel scheme has an optimal order of convergence and provide an application of it to the solution of second kind integral equations.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.2001.7599