In this paper, wavelet transform and multigrid method are combined to make the method more practical. It is known that Gaussian filtering causes shrinkage of data. To overcome this disadvantage, Gaussian filtering is ...In this paper, wavelet transform and multigrid method are combined to make the method more practical. It is known that Gaussian filtering causes shrinkage of data. To overcome this disadvantage, Gaussian filtering is replaced with wavelet transform. This method introduces no curve shrinkage. Then, the linearized form of objective equation is proposed. This makes contour matching easier to implement. Finally, the multigrid method is used to speed up the convergence.展开更多
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 mul...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.展开更多
文摘In this paper, wavelet transform and multigrid method are combined to make the method more practical. It is known that Gaussian filtering causes shrinkage of data. To overcome this disadvantage, Gaussian filtering is replaced with wavelet transform. This method introduces no curve shrinkage. Then, the linearized form of objective equation is proposed. This makes contour matching easier to implement. Finally, the multigrid method is used to speed up the convergence.
文摘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.