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.
A priori estimates on the structured conditioning of Cauchy and Vandermonde matrices
BOZZO, Enrico;FASINO, Dario
2010-01-01
Abstract
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.File in questo prodotto:
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