Preconditioners for block Toeplitz systems based on circulant preconditioners |
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Authors: | Fu-Rong Lin |
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Institution: | (1) Mathematics Department, Shantou University, Shantou 515063, Guangdong, People's Republic of China |
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Abstract: | We study the numerical solution of a block system T
m,n
x=b by preconditioned conjugate gradient methods where T
m,n
is an m×m block Toeplitz matrix with n×n Toeplitz blocks. These systems occur in a variety of applications, such as two-dimensional image processing and the discretization of two-dimensional partial differential equations. In this paper, we propose new preconditioners for block systems based on circulant preconditioners. From level-1 circulant preconditioner we construct our first preconditioner q
1(T
m,n
) which is the sum of a block Toeplitz matrix with Toeplitz blocks and a sparse matrix with Toeplitz blocks. By setting selected entries of the inverse of level-2 circulant preconditioner to zero, we get our preconditioner q
2(T
m,n
) which is a (band) block Toeplitz matrix with (band) Toeplitz blocks. Numerical results show that our preconditioners are more efficient than circulant preconditioners. |
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Keywords: | block Toeplitz system preconditioned conjugate gradient method circulant matrix Toeplitz-like matrix convergence rate |
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