We derive lower bounds for the oo-condition number of the n x n- Vandermonde matrix V,(x) in the cases where the node vector xr= [x~, x2 ..... x,] has positive elements or real elements located symmetrically with respect to the origin. The bounds obtained grow exponentially in n, with 0(2") and O(2"/2), respectively. We also compute the optimal spectral condition numbers of V.(x) for the two node configurations (including the optimal nodes) and compare them with the bounds obtained.
Lower bounds for the condition number of the Vandermonde matrix
Gabriele Inglese
1988
Abstract
We derive lower bounds for the oo-condition number of the n x n- Vandermonde matrix V,(x) in the cases where the node vector xr= [x~, x2 ..... x,] has positive elements or real elements located symmetrically with respect to the origin. The bounds obtained grow exponentially in n, with 0(2") and O(2"/2), respectively. We also compute the optimal spectral condition numbers of V.(x) for the two node configurations (including the optimal nodes) and compare them with the bounds obtained.File in questo prodotto:
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