Limits on the number of function evaluations required by certain high-dimensional integration rules of hypercubic symmetry

Author:
J. N. Lyness

Journal:
Math. Comp. **19** (1965), 638-643

MSC:
Primary 65.55

DOI:
https://doi.org/10.1090/S0025-5718-1965-0199961-5

MathSciNet review:
0199961

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Abstract: We consider an -dimensional integration rule of degree and of hypercubic symmetry. We derive theorems which set a lower bound in terms of and on the number of function evaluations such a rule requires. These results apply to spaces of integration which have hypercubic symmetry. In certain cases this bound is very close to the number of points required by a known rule.

**[1]**J. N. Lyness, "Symmetric integration rules for hypercubes. I. Error coefficients,"*Math. Comp.*, v. 19, 1965, pp. 260-276. MR**0201067 (34:952)****[2]**J. N. Lyness, "Symmetric integration rules for hypercubes. II. Rule projection and rule extension,"*Math. Comp.*, v. 19, 1965, pp. 394-407. MR**0201068 (34:953)****[3]**J. N. Lyness, "Symmetric integration rules for hypercubes. III. Construction of integration rules using null rules,"*Math. Comp.*, v. 19, 1965, pp. 625-637. MR**0201069 (34:954)****[4]**J. N. Lyness, "Integration rules of hypercubic symmetry over a certain spherically symmetric space,"*Math. Comp.*, v. 19, 1965 pp. 471-476. MR**0201070 (34:955)****[5]**A. H. Stroud & D. Secrest, "Approximate integration formulas for certain spherically symmetric regions,"*Math. Comp.*, v. 17, 1963, pp. 105-135. MR**28**#4677. MR**0161473 (28:4677)**

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DOI:
https://doi.org/10.1090/S0025-5718-1965-0199961-5

Article copyright:
© Copyright 1965
American Mathematical Society