On the approximate calculation of double integrals
HTML articles powered by AMS MathViewer
- by Moshe Levin PDF
- Math. Comp. 40 (1983), 273-282 Request permission
Abstract:
Cubature formulas are obtained which are optimal or asymptotically optimal on given sets of functions. These formulas consist of line integrals which may be evaluated by optimal or asymptotically optimal quadrature formulas. The advantage of these formulas over the optimal and asymptotically optimal cubature formulas with rectangular-lattices of knots is shown.References
- A. H. Stroud, Approximate calculation of multiple integrals, Prentice-Hall Series in Automatic Computation, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. MR 0327006
- S. L. Sobolev, Vvedenie v teoriyu kubaturnykh formul, Izdat. “Nauka”, Moscow, 1974 (Russian). MR 0478560
- Meishe Levin and Jury Girshovich, Optimal quadrature formulas, BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1979. With German, French and Russian summaries; Teubner-Texte zur Mathematik. [Teubner Texts on Mathematics]. MR 572264 S. M. Nikolsky, Quadrature Formulas, "Nauka", Moscow, 1980. (Russian)
- William J. Gordon, Distributive lattices and the approximation of multivariate functions. , Approximations with Special Emphasis on Spline Functions (Proc. Sympos. Univ. of Wisconsin, Madison, Wis., 1969) Academic Press, New York, 1969, pp. 223–277. MR 0275021
- F.-J. Delvos and H. Posdorf, $n$-th order blending, Constructive theory of functions of several variables (Proc. Conf., Math. Res. Inst., Oberwolfach, 1976) Lecture Notes in Math., Vol. 571, Springer, Berlin, 1977, pp. 53–64. MR 0487203
- J. Girshovich and M. Levin, Extremal problems for cubature formulas, Eesti NSV Tead. Akad. Toimetised Füüs.-Mat. 27 (1978), no. 2, 151–158 (English, with Russian and Estonian summaries). MR 505720
- Arthur Sard, Best approximate integration formulas; best approximation formulas, Amer. J. Math. 71 (1949), 80–91. MR 29283, DOI 10.2307/2372095 S. M. Nikolsky, "To the question of estimations of approximation with quadrature formulas," Uspekhy Mat. Nauk. v. 2 (36), 1950, pp. 165-177. (Russian)
- I. J. Schoenberg, Spline interpolation and best quadrature formulae, Bull. Amer. Math. Soc. 70 (1964), 143–148. MR 157157, DOI 10.1090/S0002-9904-1964-11054-5
- M. Levin, An extremal problem for a class of functions, Eesti NSV Tead. Akad. Toimetised Füüs.-Mat. Tehn. Tead. Seer. 12 (1963), 141–145 (Russian, with Estonian and English summaries). MR 0152151
- A. A. Žensykbaev, A property of best quadrature formulas, Mat. Zametki 23 (1978), no. 4, 551–562 (Russian). MR 493104
- Vladimir Ivanovich Krylov, Approximate calculation of integrals, The Macmillan Company, New York-London, 1962, 1962. Translated by Arthur H. Stroud. MR 0144464
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Math. Comp. 40 (1983), 273-282
- MSC: Primary 65D32; Secondary 41A55, 65D30
- DOI: https://doi.org/10.1090/S0025-5718-1983-0679445-9
- MathSciNet review: 679445