Summary
We derive lower bounds for the ∞-condition number of then×n-Vandermonde matrixV n(x) in the cases where the node vectorx T=[x1, x2,...,xn] has positive elements or real elements located symmetrically with respect to the origin. The bounds obtained grow exponentially inn. withO(2n) andO(2n/2), respectively. We also compute the optimal spectral condition numbers ofV n(x) for the two node configurations (including the optimal nodes) and compare them with the bounds obtained.
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Dedicated to the memory of James H. Wilkinson
Supported, in part, by the National Science Foundation under grant CCR-8704404
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Gautschi, W., Inglese, G. Lower bounds for the condition number of Vandermonde matrices. Numer. Math. 52, 241–250 (1987). https://doi.org/10.1007/BF01398878
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DOI: https://doi.org/10.1007/BF01398878