Note on Error Bound for Trace Approximation of Products of Toeplitz Matrices
Abstract
We investigate error orders for integral limit approximations to traces of products of Toeplitz matrices generated by integrable functions on [-π,π] having some singularities at the origin. Even though a sharp error order of the above approximation is derived in Theorem~2 of Lieberman-Phillips-2004, its proof contains an inaccuracy as pointed out by Ginovyan-Sahakyan-2013. In the present paper, we reinvestigate the claim given in Theorem~2 of Lieberman-Phillips-2004 and give an alternative proof of their claim.
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