Abstract
Recently it was shown that the ratio between the normwise Toeplitz structured condition number of a linear system and the general unstructured condition number has a finite lower bound. However, the bound was not explicit, and nothing was known about the quality of the bound. In this note we derive an explicit lower bound only depending on the dimension n, and we show that this bound is almost sharp for all n.
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Rump, S.M., Sekigawa, H. (2010). The Ratio Between the Toeplitz and the Unstructured Condition Number. In: Bini, D.A., Mehrmann, V., Olshevsky, V., Tyrtyshnikov, E.E., van Barel, M. (eds) Numerical Methods for Structured Matrices and Applications. Operator Theory: Advances and Applications, vol 199. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8996-3_18
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DOI: https://doi.org/10.1007/978-3-7643-8996-3_18
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