A note on Davis type error bounds |
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| Authors: | W Knauff A Paulik |
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| Institution: | (1) Numerische und Angewandte Mathematik, Universität Göttingen, D-3400 Göttingen, Germany |
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| Abstract: | Bounds for the error of the approximation of the value of a bounded linear functionalUf by the weighted sumU
n
f=
k
=0/n–1
a
k
f (x
k
) in Hilbert function spacesH(B) based upon the Davis method are considered. Taking into account that functionsf  H (B) withUf=U
n
f are known, improved error bounds are computed. Applying the explicit formulas numerical examples are treated and comparisons are made. |
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| Keywords: | Weight-optimal approximate rule interpolatory approximate rule reproducing kernel function Gram matrix |
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