Abstract
For a Toeplitz or Toeplitz-like matrix T, we define a preconditioning applied to the symmetrized matrix T H T, which decreases the condition number compared to the one of T H T and even the one of T. This enables us to accelerate the conjugate gradient algorithm for solving Toepiltz and Toeplitz-like linear systems, thus extending the previous results of [1], restricted to the Hermitian positive definite case. The extension relies on some recent formulae of Gohberg and Olshevsky for the inverses of Toeplitz-like matrices.
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