Block Toeplitz matrices and preconditioning
The authors investigate the asymptotic behaviour of the eigenvalues of Hermitian \(n\times n\) block Toeplitz matrices \(T_n\) with \(k\times k\) blocks, as \(n\to\infty\). They show that the spectrum of \(P^{-1}_nT_n\), where \(P_n\) is a given preconditioner, is contained in a certain interval. The limit values for both the condition numbers and the conjugate gradient convergence factor for matrices \(P^{-1}_nT_n\) are computed.
scientific article; zbMATH DE number 1186661
scientific article