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An Elementary Proof of the Exponential Conditioning of Real Vandermonde Matrices

Stefano Serra Capizzano — 2007

Bollettino dell'Unione Matematica Italiana

We provide and discuss an elementary proof of the exponential con- ditioning of real Vandermonde matrices which can be easily given in undergraduate courses: we exclusively use the definition of conditioning and the sup-norm formula on [ - 1 , 1 ] for Chebyshev polynomials of first kind. The same proof idea works virtually unchanged for the famous Hilbert matrix.

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