Symmetric integration rules for hypercubes. III. Construction of integration rules using null rules

Author:
J. N. Lyness

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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 are derived which are more economical in the number of required function evaluations than the previously published .

**[1]**J. N. Lyness,*Symmetric integration rules for hypercubes. I. Error coefficients*, Math. Comp.**19**(1965), 260–276. MR**0201067**, https://doi.org/10.1090/S0025-5718-1965-0201067-3**[2]**J. N. Lyness,*Symmetric integration rules for hypercubes. II. Rule projection and rule extension*, Math. Comp.**19**(1965), 394–407. MR**0201068**, https://doi.org/10.1090/S0025-5718-1965-0201068-5**[3]**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.

Retrieve articles in *Mathematics of Computation*
with MSC:
65.55

Retrieve articles in all journals with MSC: 65.55

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1965-0201069-7

Article copyright:
© Copyright 1965
American Mathematical Society