A proposal for toeplitz matrix calculations
Studies in Applied Mathematics
Circulant preconditioners for Hermitian Toeplitz systems
SIAM Journal on Matrix Analysis and Applications
FFT-based preconditioners for Toeplitz-block least squares problems
SIAM Journal on Numerical Analysis
Regularizing inverse preconditioners for symmetric band Toeplitz matrices
EURASIP Journal on Applied Signal Processing
A generalization of the optimal diagonal approximate inverse preconditioner
Computers & Mathematics with Applications
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Customary circulant preconditioners of Chan, Strang, and inverse-Toeplitz type aremodified for the regularized solution of ill-conditioned Toeplitz systems. Given a symmetric two-level Toeplitz matrix A, and two parameters @t and @s, consider the customary preconditioner C and modify it by replacing its eigenvalues with modulus less than @t with the value @s. The circulant matrix obtained in this way is used as a preconditioner. We analyze the distribution of the eigenvalues of the preconditioned matrix and the regularization properties. Numerical experiments, shown for the image restoration problem, validate the theoretical results.