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- W2034367460 abstract "Research on preconditioning Toeplitz matrices with circulant matrices has been active recently. The preconditioning technique can be easily generalized to block Toeplitz matrices. That is, for a block Toeplitz matrix T consisting of $N times N$ blocks with $M times M$ elements per block, a block circulant matrix R is used with the same block structure as its preconditioner. In this research, the spectral clustering property of the preconditioned matrix $R^{ - 1} T$ with T generated by two-dimensional rational functions $T(z_x ,z_y )$ of order $(p_x ,q_x ,p_y ,q_y )$ is examined. It is shown that the eigenvalues of $R^{ - 1} T$ are clustered around unity except at most $O(Mgamma _y + Ngamma _x )$ outliers, where $gamma _x = max (p_x ,q_x )$ and $gamma _y = max (p_y ,q_y )$. Furthermore, if T is separable, the outliers are clustered together such that $R^{ - 1} T$ has at most $(2gamma _x + 1)(2gamma _y + 1)$ asymptotic distinct eigenvalues. The superior convergence behavior of the preconditioned c..." @default.
- W2034367460 created "2016-06-24" @default.
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- W2034367460 date "1992-07-01" @default.
- W2034367460 modified "2023-09-23" @default.
- W2034367460 title "On the Spectrum of a Family of Preconditioned Block Toeplitz Matrices" @default.
- W2034367460 doi "https://doi.org/10.1137/0913056" @default.
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