1. GMRES PRECONDICIONADO CON WAVELETS. UN ALGORITMO DE SELECCIÓN DEL UMBRAL PARA LA OBTENCIÓN DEL PATRÓN DE DISPERSIÓN.
- Author
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Villarín Pildaín, Lilian, León Mecías, Angela, Díaz Romañach, Marta L. Baguer, and Linares Zaila, Yisleidy
- Subjects
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GENERALIZED minimal residual method , *LINEAR equations , *HAAR system (Mathematics) , *WAVELETS (Mathematics) , *SPARSE matrices , *KRYLOV subspace - Abstract
In order to use the GMRES method to solve dense linear equations systems in O(n) iterations, the building of a preconditioner using the no singular sparse approximation of a dense linear equations systems matrix is proposed. The sparse approximation is obtained by wavelet compression, using Haar and Daubechies wavelets basis. The novelty of this work is the proposed strategy to automatic selection of the threshold to obtain the sparse matrix from the original dense matrix, which is based on statistics concept of percentile and another contribution is the cost analysis that was done. A broad numerical experimentation allowed to evaluate the quality of the preconditioner related to some parameters like problem dimension, used wavelet base and number of non zero elements of the sparse matrix. [ABSTRACT FROM AUTHOR]
- Published
- 2012