On the Complexity of the Preconditioned Conjugate Gradient Algorithm for Solving Toeplitz Systems with a Fisher--Hartwig Singularity

The Toeplitz matrix $T_n$ with generating function $f ( \omega ) = |1 - e ^{-i \omega}|^{-2d} h( \omega )$, where $d \in (-\frac{1}{2}, \frac{1}{2})\setminus \{0\}$ and $h(\omega)$ is positive, continuous on $[-\pi,\pi]$, and differentiable on $[-\pi,\pi]\setminus\{0\}$, has a Fisher--Hartwig singul...

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