An error analysis for numerical multiple integration. I
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References
-
R. E. Barnhill, Numerical Contour Integration U. S. Army Mathematics Research Center Report No. 519, Madison, Wis., 1964.
- Robert E. Barnhill, Complex quadratures with remainders of minimum norm, Numer. Math. 7 (1965), 384–390. MR 191088, DOI 10.1007/BF01436250
- R. E. Barnhill and J. A. Wixom, Quadratures with remainders of minimum norm. I, Math. Comp. 21 (1967), 66–75. MR 223089, DOI 10.1090/S0025-5718-1967-0223089-0
- R. E. Barnhill and J. A. Wixom, Quadratures with remainders of minimum norm. II, Math. Comp. 21 (1967), 382–387. MR 223090, DOI 10.1090/S0025-5718-1967-0223090-7 R. E. Barnhill, "Optimal quadratures in ${L^2}({E_p})$. I," SI AM J. Numer. Anal., v. 4, 1967, pp. 390–397. R. E. Barnhill, "Optimal quadratures in ${L^2}({E_p})$. II." SIAM J. Numer. Anal. (To appear.) R. E. Barnhill, "Asymptotic properties of minimum norm and optimal quadratures." (Submitted for publication.)
- Stefan Bergman, The Kernel Function and Conformal Mapping, Mathematical Surveys, No. 5, American Mathematical Society, New York, N. Y., 1950. MR 0038439 G. Birkhoff & C. R. deBoor, "Piecewise polynomial interpolation and approximation," Approximation of Functions, edited by H. L. Garabedian, Elsevier, Amsterdam, 1965. MR 32 #2789.
- Salomon Bochner and William Ted Martin, Several Complex Variables, Princeton Mathematical Series, vol. 10, Princeton University Press, Princeton, N. J., 1948. MR 0027863
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
- Philip Davis, Errors of numerical approximation for analytic functions, J. Rational Mech. Anal. 2 (1953), 303–313. MR 54348, DOI 10.1512/iumj.1953.2.52016
- Philip J. Davis, Errors of numerical approximation for analytic functions, Survey of numerical analysis, McGraw-Hill, New York, 1962, pp. 468–484. MR 0135721
- Philip J. Davis, Interpolation and approximation, Blaisdell Publishing Co. [Ginn and Co.], New York-Toronto-London, 1963. MR 0157156
- Philip J. Davis and Philip Rabinowitz, Numerical integration, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1967. MR 0211604
- 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
- Michael Golomb and Hans F. Weinberger, Optimal approximation and error bounds, On numerical approximation. Proceedings of a Symposium, Madison, April 21-23, 1958, Publication of the Mathematics Research Center, U.S. Army, the University of Wisconsin, no. 1, University of Wisconsin Press, Madison, Wis., 1959, pp. 117–190. Edited by R. E. Langer. MR 0121970 M. Golomb, Lectures on Theory of Approximation, Argonne National Laboratory, Argonne, 111., 1962.
- Preston C. Hammer and Arthur H. Stroud, Numerical evaluation of multiple integrals. II, Math. Tables Aids Comput. 12 (1958), 272–280. MR 102176, DOI 10.1090/S0025-5718-1958-0102176-6
- Preston C. Hammer, Numerical evaluation of multiple integrals, On numerical approximation. Proceedings of a Symposium, Madison, April 21-23, 1958, Publication of the Mathematics Research Center, U.S. Army, the University of Wisconsin, no. 1, University of Wisconsin Press, Madison, Wis., 1959, pp. 99–115. Edited by R. E. Langer. MR 0100355
- Vladimir Ivanovich Krylov, Approximate calculation of integrals, The Macmillan Company, New York-London, 1962, 1962. Translated by Arthur H. Stroud. MR 0144464
- J. N. Lyness, Symmetric integration rules for hypercubes. I. Error coefficients, Math. Comp. 19 (1965), 260–276. MR 201067, DOI 10.1090/S0025-5718-1965-0201067-3
- J. Meinguet, Methods for estimating the remainder in linear rules of approximation. Application to the Romberg algorithm, Numer. Math. 8 (1966), 345–366. MR 199962, DOI 10.1007/BF02162979
- Arthur Sard, Linear approximation, American Mathematical Society, Providence, R.I., 1963. MR 0158203
- D. D. Stancu, The remainder of certain linear approximation formulas in two variables, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 1 (1964), 137–163. MR 177240
- Frank Stenger, Bounds on the error of Gauss-type quadratures, Numer. Math. 8 (1966), 150–160. MR 196936, DOI 10.1007/BF02163184
- Frank Stenger, Error bounds for the evaluation of integrals by repeated Gauss-type formulae, Numer. Math. 9 (1966), 200–213. MR 205462, DOI 10.1007/BF02162084
- Arthur H. Stroud, Quadrature methods for functions of more than one variable, Ann. New York Acad. Sci. 86 (1960), 776–791 (1960). MR 119417
- A. H. Stroud and Don Secrest, Gaussian quadrature formulas, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1966. MR 0202312 R. A. Valentin, Applications of Functional Analysis to Optimal Numerical Approximation for Analytic Functions, Ph.D. Thesis, Brown University, Providence, R. I., 1965.
- Hiroki Yanagihara, A new method of numerical integration of Gaussian type, Bull. Fukuoka Gakugei Univ. III 6 (1956), 19–25 (Japanese). MR 0148221 G. Hämmerlin, "Über ableitungsfreie Schranken für Quadraturfehler," Numer. Math., v. 5, 1963, pp. 226–233. MR 28 #1756.
- Günther Hämmerlin, Über ableitungsfreie Schranken für Quadraturfehler. II. Ergänzungen und Möglichkeiten zur Verbesserung, Numer. Math. 7 (1965), 232–237 (German). MR 184427, DOI 10.1007/BF01436079
- Günther Hämmerlin, Zur Abschätzung von Quadraturfehlern für analytische Funktionen, Numer. Math. 8 (1966), 334–344 (German). MR 202306, DOI 10.1007/BF02162978
Additional Information
- © Copyright 1968 American Mathematical Society
- Journal: Math. Comp. 22 (1968), 98-109
- MSC: Primary 65.55
- DOI: https://doi.org/10.1090/S0025-5718-1968-0226852-6
- MathSciNet review: 0226852