The optimal preconditioner of strictly diagonally dominant <Emphasis Type="Italic">Z</Emphasis>-matrix |
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Authors: | Ji-cheng Li Wei Li |
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Institution: | (1) Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049, China |
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Abstract: | In this paper, we present a series of new preconditioners with parameters of strictly diagonally dominant Z-matrix, which contain properly two kinds of known preconditioners as special cases. Moreover, we prove the monotonicity of
spectral radiuses of iterative matrices with respect to the parameters and some comparison theorems. The results obtained
show that the bigger the parameter k is(i.e., we select the more upper right diagonal elements to be the preconditioner), the less the spectral radius of iterative
matrix is. A numerical example generated randomly is provided to illustrate the theoretical results.
Supported by Shaanxi Province Natural Science Foundation, 2007A16, China |
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Keywords: | Preconditioned method iteration splitting linear system |
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