On the monotonicity of sequences of quadrature formulae |
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| Authors: | Geno Nikolov |
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| Institution: | (1) Department of Mathematics, University of Sofia, Boul. A. Ivanov 5, 1126 Sofia, Bulgaria |
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| Abstract: | Summary LetI(f) L(f)=
k=0
r
 =0
vk–1
a
k
f
()(X
k
) be a quadrature formula, and let {S
n
(f)}
n=1
be successive approximations of the definite integralI(f)=
0
1
f(x)dx obtained by the composition ofL, i.e.,S
n(f)=L(
n
), where
.We prove sufficient conditions for monotonicity of the sequence {S
n
(f)}
n=1
. As particular cases the monotonicity of well-known Newton-Cotes and Gauss quadratures is shown. Finally, a recovery theorem based on the monotonicity results is presented |
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| Keywords: | 65D30 |
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