Minimal quadratures for functions of low-order continuity
Authors:
L. W. Johnson and R. D. Riess
Journal:
Math. Comp. 25 (1971), 831-835
MSC:
Primary 65D30
DOI:
https://doi.org/10.1090/S0025-5718-1971-0298940-X
MathSciNet review:
0298940
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Abstract | References | Similar Articles | Additional Information
Abstract: An analog of Wilf’s quadrature is developed for functions of low-order continuity. This analog is used to demonstrate that the order of convergence of Wilf’s quadrature is at least $1/n$.
- R. E. Barnhill, J. E. Dennis Jr., and G. M. Nielson, A new type of Chebyshev quadrature, Math. Comp. 23 (1969), 437–441. MR 242367, DOI https://doi.org/10.1090/S0025-5718-1969-0242367-4
- Ulrich Eckhardt, Einige Eigenschaften Wilfscher Quadraturformeln, Numer. Math. 12 (1968), 1–7 (German). MR 256561, DOI https://doi.org/10.1007/BF02170990
- David Elliott, Chebyshev series method for the numerical solution of Fredholm integral equations, Comput. J. 6 (1963/64), 102–111. MR 155452, DOI https://doi.org/10.1093/comjnl/6.1.102
- J. P. Imhof, On the method for numerical integration of Clenshaw and Curtis, Numer. Math. 5 (1963), 138–141. MR 157482, DOI https://doi.org/10.1007/BF01385885
- Philip Rabinowitz, Error bounds in Gaussian integration of functions of low-order continuity, Math. Comp. 22 (1968), 431–434. MR 226861, DOI https://doi.org/10.1090/S0025-5718-1968-0226861-7
- Nira Richter, Properties of minimal integration rules, SIAM J. Numer. Anal. 7 (1970), 67–79. MR 260176, DOI https://doi.org/10.1137/0707003
- Herbert S. Wilf, Exactness conditions in numerical quadrature, Numer. Math. 6 (1964), 315–319. MR 179941, DOI https://doi.org/10.1007/BF01386079
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Additional Information
Keywords:
Wilf’s quadrature,
optimal quadrature,
order of convergence,
low-order continuity
Article copyright:
© Copyright 1971
American Mathematical Society
