A Priori Estimates on the Structured Conditioning of Cauchy and Vandermonde Matrices
We analyze the componentwise and normwise sensitivity of inverses of Cauchy, Vandermonde, and Cauchy-Vandermonde matrices, with respect to relative componentwise perturbations in the nodes defining these matrices. We obtain a priori, easily computable upper bounds for these condition numbers. In particular, we improve known estimates for Vandermonde matrices with generic real nodes; twe consider in detail Vandermonde matrices with nonnegative or symmetric nodes; and we extend the analysis to the class of complex Cauchy-Vandermonde matrices.
Mathematics Subject Classification (2000)Primary 15A12 Secondary 15A57 65F35
KeywordsCondition number displacement structure Cauchy matrix Vandermonde matrix
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