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Biorthogonal Wavelet Based Algebraic Multigrid Preconditioners for Large Sparse Linear Systems
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Applied Mathematics·Volume 02 (2011)·Pages 1378–1381·Published 30 November 2011·DOI10.4236/am.2011.211194
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Abstract
In this article algebraic multigrid as preconditioners are designed, with biorthogonal wavelets, as intergrid operators for the Krylov subspace iterative methods. Construction of hierarchy of matrices in algebraic multigrid context is based on lowpass filter version of Wavelet Transform. The robustness and efficiency of this new approach is tested by applying it to large sparse, unsymmetric and ill-conditioned matrices from Tim Davis collection of sparse matrices. Proposed preconditioners have potential in reducing cputime, operator complexity and storage space of algebraic multigrid V-cycle and meet the desired accuracy of solution compared with that of orthogonal wavelets.
KeywordsAlgebraic MultigridPreconditionerWavelet TransformSparse MatrixKrylov Subspace Iterative Methods
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