The optimum addition of points to quadrature formulae
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- by T. N. L. Patterson PDF
- Math. Comp. 22 (1968), 847-856 Request permission
Erratum: Math. Comp. 23 (1969), 892.
Abstract:
Methods are developed for the addition of points in an optimum manner to the Gauss, Lobatto and general quadrature formulae. A new set of $n$-point formulae are derived of degree $(3n - 1)/2$.References
- Aleksandr Semenovich Kronrod, Nodes and weights of quadrature formulas. Sixteen-place tables, Consultants Bureau, New York, 1965. Authorized translation from the Russian. MR 0183116 E. W. Hobson, Spherical and Ellipsoidal Harmonics, Cambridge Univ. Press, New York, 1931.
- T. N. L. Patterson, On some Gauss and Lobatto based integration formulae, Math. Comp. 22 (1968), 877–881; addendum, ibid. 22 (1968), no. 104, loose microfiche suppl., D1–D4. MR 0240983, DOI 10.1090/S0025-5718-68-99865-7
- P. Davis and P. Rabinowitz, On the estimation of quadrature errors for analytic functions, Math. Tables Aids Comput. 8 (1954), 193–203. MR 65256, DOI 10.1090/S0025-5718-1954-0065256-6
- C. W. Clenshaw and A. R. Curtis, A method for numerical integration on an automatic computer, Numer. Math. 2 (1960), 197–205. MR 117885, DOI 10.1007/BF01386223
Additional Information
- © Copyright 1968 American Mathematical Society
- Journal: Math. Comp. 22 (1968), 847-856
- DOI: https://doi.org/10.1090/S0025-5718-68-99866-9
- MathSciNet review: 0242370