On the approximate calculation of double integrals

Author:
Moshe Levin

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

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Abstract | References | Similar Articles | Additional Information

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.

- A. H. Stroud,
*Approximate calculation of multiple integrals*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. Prentice-Hall Series in Automatic Computation. 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, - 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) Springer, Berlin, 1977, pp. 53–64. Lecture Notes in Math., Vol. 571. 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 https://doi.org/10.2307/2372095
S. M. Nikolsky, "To the question of estimations of approximation with quadrature formulas," - I. J. Schoenberg,
*Spline interpolation and best quadrature formulae*, Bull. Amer. Math. Soc.**70**(1964), 143–148. MR**157157**, DOI https://doi.org/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 Co., New York-London, 1962, 1962. Translated by Arthur H. Stroud. MR**0144464**

*Quadrature Formulas*, "Nauka", Moscow, 1980. (Russian)

*Uspekhy Mat. Nauk.*v. 2 (36), 1950, pp. 165-177. (Russian)

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Article copyright:
© Copyright 1983
American Mathematical Society