A. Genz and R. Cools. An adaptive numerical cubature algorithm for simplices. Technical report, Department of Computer Science, K. U. Leuven, 1997. Home/Search Document Details and Download
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Quasi Monte Carlo Evaluation of Sensitivities of Options.. - Benth, Dahl, Karlsen (Correct)
....by the number L i ) to use in each of them. Alternative approaches use information from the integrand to develop approximations of the integral in sub domains with a deterministic approach rather than with simulation. This is done in e.g. Berntsen, Espelid and Genz [2] Cools [5] Genz and Cools [10], and Press and Farrar [17] We represent the domain decomposition by a binary tree. Each leaf node in the tree corresponds to a distinct part of the domain, and when we expand the tree we divide the domain represented by a node in two parts of equal size. For one dimensional integrands, the ....
A. Genz and R. Cools. An adaptive numerical cubature algorithm for simplices. Technical report, Department of Computer Science, K. U. Leuven, 1997.
Monomial cubature rules since "Stroud": a compilation - part 2 - Cools (1999) (8 citations) Self-citation (Cools) (Correct)
.... 5) 7 123 (n = 5) NO if 5 n 12 [115] new (n 3 9n 2 14n 9) 3; n 6 NI if 13 n 40 S n (n 5) 7 123 (n = 5) NO if 5 n 7 [115] new (n 3 9n 2 14n 9) 3; n 6 NI if 8 n 40 T n (4 n 12) 4 (n 2 3n 4) 2 I [113] new T n (n 4) 7 (n 3 12n 2 29n 24) 6 I [113, 105] new For completeness we mention that the formula for T n in [105] was copied from Mysovskikh s work. Embedded cubature formulae Region Degrees N Quality References Remark E r 2 n 1 3 Delta Delta Delta 51 See ( 106] p. 305) 2) 106] new 3 Three special cubature rules As a rule, ....
.... n 6 NI if 13 n 40 S n (n 5) 7 123 (n = 5) NO if 5 n 7 [115] new (n 3 9n 2 14n 9) 3; n 6 NI if 8 n 40 T n (4 n 12) 4 (n 2 3n 4) 2 I [113] new T n (n 4) 7 (n 3 12n 2 29n 24) 6 I [113, 105] new For completeness we mention that the formula for T n in [105] was copied from Mysovskikh s work. Embedded cubature formulae Region Degrees N Quality References Remark E r 2 n 1 3 Delta Delta Delta 51 See ( 106] p. 305) 2) 106] new 3 Three special cubature rules As a rule, we ignored the Russian and other non western literature except when ....
A. Genz and R. Cools, An adaptive numerical cubature algorithm for simplices, Report TW 273, Dept. of Computer Science, K.U.Leuven, 1997.
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