How bad are Hankel matrices? |
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Authors: | Evgenij E Tyrtyshnikov |
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Institution: | (1) Institute of Numerical Mathematics, Russian Academy of Sciences, Leninskij Prosp., 32-A, Moscow 117334, Russia , RU |
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Abstract: | Summary. Considered are Hankel, Vandermonde, and Krylov basis matrices.
It is proved that for any real positive definite Hankel matrix
of order , its spectral condition number is bounded from below
by
. Also proved is that the spectral condition
number of a Krylov basis matrix is bounded from below by
. For , a Vandermonde matrix with arbitrary but pairwise
distinct nodes , we show that ; if either or
for all , then .
Received January 24, 1993/Revised version received July 19, 1993 |
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Keywords: | Mathematics Subject Classification (1991): 65F10 65F99 |
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