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V. M. Garcia, L. Acevedo and A. M. Vidal, “Variants of Algebraic Wavelet Based Multigrid Methods: Applications to Shifted Linear Systems,” Applied Mathematics and Computation, Vol. 202, No. 1, 2008, pp. 287-299. doi:10.1016/j.amc.2008.02.015

has been cited by the following article:

• TITLE: Biorthogonal Wavelet Based Algebraic Multigrid Preconditioners for Large Sparse Linear Systems

  AUTHORS: A. Padmanabha Reddy, Nagendrappa M. Bujurke

  KEYWORDS: Algebraic Multigrid, Preconditioner; Wavelet Transform, Sparse Matrix, Krylov Subspace Iterative Methods

  JOURNAL NAME: Applied Mathematics, Vol.2 No.11, November 30, 2011

  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.