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.**19**(1965), 260–276. MR**201067**, 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**201068**, https://doi.org/10.1090/S0025-5718-1965-0201068-5**[3]**J. N. Lyness,*Symmetric integration rules for hypercubes. III. Construction of integration rules using null rules*, Math. Comp.**19**(1965), 625–637. MR**201069**, https://doi.org/10.1090/S0025-5718-1965-0201069-7**[4]**J. N. Lyness,*Integration rules of hypercubic symmetry over a certain spherically symmetric space*, Math. Comp.**19**(1965), 471–476. MR**201070**, https://doi.org/10.1090/S0025-5718-1965-0201070-3**[5]**A. H. Stroud and Don Secrest,*Approximate integration formulas for certain spherically symmetric regions*, Math. Comp.**17**(1963), 105–135. MR**161473**, https://doi.org/10.1090/S0025-5718-1963-0161473-0

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

Article copyright:
© Copyright 1965
American Mathematical Society