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- W2042634710 abstract "A particular subdivision of a simplex $S_n $ into $m^n $ subsimplices of equal n-volume is described. The $m^n $-copy quadrature rule $Q^{(m)} (S_n )$ is defined in terms of a set ${ Q} $ of n! simplex quadrature rules, one for each distinct type of subsimplex occurring in the subdivision. An n-dimensional analogue of the Euler–Maclaurin asymptotic expansion for the simplex valid for analytic integrand functions $phi $ and any quadrature rule set ${ Q} $ is derived by integrating the representation for $phi ({bf x})$ obtained in Part 1. This has the form[{{Q^{(m)} (S_n )phi - I(S_n )phi simeq Sigma A_q (Q;phi )} / {m^q }}] and terminates when $phi ({bf x})$ is a polynomial. For rule sets based on many familiar simplex rules, the odd terms vanish leaving an even expansion" @default.
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- W2042634710 date "1978-10-01" @default.
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- W2042634710 title "Quadrature over a Simplex: Part 2. A Representation for the Error Functional" @default.
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- W2042634710 doi "https://doi.org/10.1137/0715057" @default.
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