Some Aspects of Circulant Preconditioners
Copyright policy )Some Aspects of Circulant Preconditioners
If \(T\) is a given \(n\times n\) Hermitian Toeplitz matrix, the circulant matrix \(C_ 0\) is determined which minimizes \(\| I-C^{-1/2}TC^{- 1/2}\|_ F\) among all circulant matrices \(C\). It is shown that \(C_ 0\) can be computed in \(O(n\log n)\) operations and that the eigenvalues of \(C_ 0^ 1T\) are asymptotically clustered around \(z=1\). In addition, circulant approximants to Toeplitz matrices with respect to other norms (than \(\| \cdot\|_ F\)) are studied.
circulant matrix, Iterative numerical methods for linear systems, preconditioned conjugate gradient method, Numerical computation of matrix norms, conditioning, scaling, Hermitian Toeplitz matrix
circulant matrix, Iterative numerical methods for linear systems, preconditioned conjugate gradient method, Numerical computation of matrix norms, conditioning, scaling, Hermitian Toeplitz matrix
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