An estimate of goodness of cubatures for the unit circle in

Author:
J. I. Maeztu

Journal:
Math. Comp. **47** (1986), 651-658

MSC:
Primary 65D32

DOI:
https://doi.org/10.1090/S0025-5718-1986-0856709-X

MathSciNet review:
856709

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The Sarma-Eberlein estimate is an estimate of goodness of cubature formulae for *n*-cubes defined as the integral of the square of the formula truncation error, over a function space provided with a measure. In this paper, cubature formulae for the unit circle in are considered and an estimate of the above type is constructed with the desirable property of being compatible with the symmetry group of the circle.

**[1]**H. S. M. Coxeter,*Introduction to geometry*, 2nd ed., John Wiley & Sons, Inc., New York-London-Sydney, 1969. MR**0346644****[2]**Derek John Scott Robinson,*A course in the theory of groups*, Graduate Texts in Mathematics, vol. 80, Springer-Verlag, New York-Berlin, 1982. MR**648604****[3]**V. L. N. Sarma,*A generalisation of Eberlein’s integral over function space*, Trans. Amer. Math. Soc.**121**(1966), 52–61. MR**0193494**, https://doi.org/10.1090/S0002-9947-1966-0193494-5**[4]**V. L. N. Sarma,*Eberlein measure and mechanical quadrature formulae. I. Basic theory.*, Math. Comp.**22**(1968), 607–616. MR**0253559**, https://doi.org/10.1090/S0025-5718-1968-0253559-1**[5]**V. L. N. Sarma and A. H. Stroud,*Eberlein measure and mechanical quadrature formulae II. Numerical results*, Math. Comp.**23**(1969), 781–784. MR**0258282**, https://doi.org/10.1090/S0025-5718-1969-0258282-6**[6]**A. H. Stroud,*Approximate calculation of multiple integrals*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. Prentice-Hall Series in Automatic Computation. MR**0327006**

Retrieve articles in *Mathematics of Computation*
with MSC:
65D32

Retrieve articles in all journals with MSC: 65D32

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1986-0856709-X

Article copyright:
© Copyright 1986
American Mathematical Society