Electronic Resource
Springer
Numerische Mathematik
62 (1992), S. 557-565
ISSN:
0945-3245
Keywords:
65D30
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary LetI(f)≈L(f)=∑ k=0 r ∑ λ=0 vk−1 a kλ f (λ)(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(ϕ n ), where $$\varphi _n (x) = \frac{1}{n}\sum\nolimits_{k = 0}^{n - 1} {f\left( {\frac{{k + x}}{n}} \right)} $$ . 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
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01396243
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