Symmetric integration rules for hypercubes. III. Construction of integration rules using null rules
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- by J. N. Lyness PDF
- Math. Comp. 19 (1965), 625-637 Request permission
Abstract:
A new operator, which we term a "Null Rule" is defined. Its properties which are analogous to those of an integration rule are investigated. It is found to be useful in the construction of high-dimensional integration rules of moderate degree. A set of integration rules $W_{t + 1}^{(n)}$ are derived which are more economical in the number of required function evaluations than the previously published $\bar G_{t + 1}^{(n)}$.References
- J. N. Lyness, Symmetric integration rules for hypercubes. I. Error coefficients, Math. Comp. 19 (1965), 260–276. MR 201067, DOI 10.1090/S0025-5718-1965-0201067-3
- J. N. Lyness, Symmetric integration rules for hypercubes. II. Rule projection and rule extension, Math. Comp. 19 (1965), 394–407. MR 201068, DOI 10.1090/S0025-5718-1965-0201068-5 J. N. Lyness, "Limits on the number of function evaluations required by certain highdimensional integration rules of hypercubic symmetry," Math. Comp., v. 19, pp. 638–643.
Additional Information
- © Copyright 1965 American Mathematical Society
- Journal: Math. Comp. 19 (1965), 625-637
- MSC: Primary 65.55
- DOI: https://doi.org/10.1090/S0025-5718-1965-0201069-7
- MathSciNet review: 0201069