A CONSTRAINT ON EXTENSIBLE QUADRATURE RULES By Art
نویسندگان
چکیده
When the worst case integration error in a family of functions decays as n−α for some α > 1 and simple averages along an extensible sequence match that rate at a set of sample sizes n1 < n2 < · · · < ∞, then these sample sizes must grow at least geometrically. More precisely, nk+1/nk ≥ ρmust hold for a value 1 < ρ < 2 that increases with α. This result always rules out arithmetic sequences but never rules out sample size doubling. The same constraint holds in a root mean square setting.
منابع مشابه
A constraint on extensible quadrature rules
When the worst case integration error in a family of functions decays as n−α for some α > 1 and simple averages along an extensible sequence match that rate at a set of sample sizes n1 < n2 < · · · < ∞, then these sample sizes must grow at least geometrically. More precisely, nk+1/nk ≥ ρmust hold for a value 1 < ρ < 2 that increases with α. This result always rules out arithmetic sequences but ...
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