Geodesic
Computational investigation of $\mathrm{IWZ}(k)$ precondition
Matematičeskoe modelirovanie, Tome 26 (2014) no. 11, pp. 97-100.

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Construction of effective preconditions for acceleration of iterative methods of system of linear equations solution is a topical issue of modern computing mathematics. There are wide-spread preconditions on the basis of various incomplete decompositions of system matrix. This paper is devoted to the construction and investigation of a new precondition on the basis of an incomplete $\mathrm{WZ}$-factorization. This precondition is a generalization of the previously described $\mathrm{IWZ(0)}$ precondition. In $\mathrm{IWZ(0)}$ all elements of $W$ and $Z$ multipliers in the positions that do not belong to the picture of system matrix, are zeroed. In a new precondition each raw of an assembly matrix $F=W+Z-E$ except for elements that belong to the picture of system matrix, consist of the $k$ biggest elements that belong to the remaining positions. This precondition was named $\mathrm{ILU}(k)$. The work presents the results of computing experiments with the precondition that has been used for accelerating BICG method. Systems with randomly generated disperse matrix were used as test systems. Matrix had set spectral properties. It has been shown that in different problems a new precondition was more effective than $\mathrm{IWZ (0)}$. The realization of BICG method and the above mentioned preconditions in C programming language were written by the author.
Keywords: WZ-factorization, preconditioning, iterative methods for SLAE solving, computational linear algebra. 
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     author = {I. M. Nikolsky},
     title = {Computational investigation of $\mathrm{IWZ}(k)$ precondition},
     journal = {Matemati\v{c}eskoe modelirovanie},
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     url = {http://geodesic.mathdoc.fr/item/MM_2014_26_11_a14/}
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I. M. Nikolsky. Computational investigation of $\mathrm{IWZ}(k)$ precondition. Matematičeskoe modelirovanie, Tome 26 (2014) no. 11, pp. 97-100. http://geodesic.mathdoc.fr/item/MM_2014_26_11_a14/

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