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Monomial cubature rules since “Stroud”: A compilation. II. (English) Zbl 0954.65021
[For part I see R. Cools and P. Rabinowitz, ibid. 48, No. 3, 309-329 (1993; Zbl 0799.65027).]
This second part of a compilation of rules for multiple integration continues in the same format as the original. New rules, new references and some corrections are reported mostly in tabular form to clearly correlate with the previous tables. An appropriate commentary accompanies the tables. The references also augment the earlier set with numbering running on consecutively.
The two parts together, and with A. H. Stroud’s book [Approximate calculation of multiple integrals (1971; Zbl 0379.65013)], then give a near comprehensive listing, at least of work available in English. As before, the regions covered are the \(n\)-cube, \(n\)-sphere and the entire space for selected low values of \(n\). Some results for general \(n\) are also included.

MSC:
65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures
41A63 Multidimensional problems
Software:
adsimp; HRMSYM; PATSYM
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References:
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