On the condition numbers of large semidefinite Toeplitz matrices Original Research Article

This paper is devoted to asymptotic estimates for the (spectral or Euclidean) condition numbers κ(Tn(a)) = short parallelTn(a)short parallel short parallelT−1n(a)short parallel of large n × n Toeplitz matrices Tn(a) in the case where the symbol a is an L∞ function and Re a ≥ 0 almost everywhere. We describe several classes of symbols a for which κ(Tn(a)) increases like (log n)x, nx, or even exn.