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- W1017306734 abstract "Given a mass distribution dσ(x) on the (finite or infinite) interval (a,b), where σ(x) has at least n+1 points of increase, and assuming the existence of the first 2n moments of dσ(x), $${mu _k} = int_a^b {{x^k}} dsigma (x),;;;;k = 0,1,2,...,2n - 1$$(1.1)it is well known that the n-point Gaussian quadrature rule associated with the distribution da(x) exists and is unique. That is, there exist unique nodes v (n) ∊ (a,b) and weights λ v (n) > 0 such that $$int_a^b {f(x)} dsigma (x) = sumlimits_{v = 1}^n {lambda _v^{(n)}f(xi _v^{(n)})} + {R_n}(f)$$(1.2)with $$ {R_n}(f) = 0,for,all,f in {P_{2n - 1}} $$(1.3)." @default.
- W1017306734 created "2016-06-24" @default.
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- W1017306734 date "1979-01-01" @default.
- W1017306734 modified "2023-09-26" @default.
- W1017306734 title "On Generating Gaussian Quadrature Rules" @default.
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- W1017306734 doi "https://doi.org/10.1007/978-3-0348-6288-2_10" @default.
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