We provide and discuss an elementary proof of the exponential conditioning 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 Hubert matrix.
An elementary proof of the exponential conditioning of real Vandermonde matrices
SERRA CAPIZZANO, STEFANO
2007-01-01
Abstract
We provide and discuss an elementary proof of the exponential conditioning 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 Hubert matrix.
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