Adaptive filtering. (English) Zbl 0897.65027

The adaptive filtering method which leads to robust algorithms for the solution of systems of linear equations arising from the discretization of partial differential equations with strongly varying coefficients is introduced and analyzed. The basis of these algorithms is the tangential frequency filtering decomposition whose theoretical results are summarized in Section 2. The adaptive test vector iterative method is introduced in Section 3. In Section 4, the new test vectors which are produced by the adaptive test vector algorithm are analyzed. In the last section, some numerical experiments illustrate the efficiency and the robustness of these algorithms.


65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
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