Adaptive filtering

Christian Wagner*, Gabriel Wittum

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


In this paper, the adaptive filtering method is introduced and analysed. This method leads to robust algorithms for the solution of systems of linear equations which arise from the discretisation of partial differential equations with strongly varying coefficients. These iterative algorithms are based on the tangential frequency filtering decompositions (TFFD). During the iteration with a preliminary preconditioner, the adaptive test vector method calculates new test vectors for the TFFD. The adaptive test vector iterative method allows the combination of the tangential frequency decomposition and other iterative methods such as multi-grid. The connection with the TFFD improves the robustness of these iterative methods with respect to varying coefficients. Interface problems as well as problems with stochastically distributed properties are considered. Realistic numerical experiments confirm the efficiency of the presented algorithms.

Original languageEnglish (US)
Pages (from-to)305-328
Number of pages24
JournalNumerische Mathematik
Issue number2
StatePublished - Jan 1 1997

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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