A fast, preconditioned conjugate gradient Toeplitz and Toeplitz-like solvers

For a Toeplitz or Toeplitz-like matrix T, we define a preconditioning applied to the symmetrized matrix THT, which decreases the condition number compared to the one of THT 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.