An error analysis for numerical multiple integration. II

Author:
Robert E. Barnhill

Journal:
Math. Comp. **22** (1968), 286-292

MSC:
Primary 65.55

MathSciNet review:
0230465

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References | Similar Articles | Additional Information

**[1]**R. E. Barnhill and J. A. Wixom,*Quadratures with remainders of minimum norm. I*, Math. Comp.**21**(1967), 66–75. MR**0223089**, 10.1090/S0025-5718-1967-0223089-0**[2]**R. E. Barnhill, "Optimal quadratures in . I,"*SIAM J. Numer. Anal.*, v. 4, 1967, pp. 390-397.**[3]**R. E. Barnhill, "Optimal quadratures in . II,"*SIAM J. Numer. Anal.*(To appear.)**[4]**Robert E. Barnhill,*Asymptotic properties of minimum norm and optimal quadratures*, Numer. Math.**12**(1968), 384–393. MR**0243739****[5]**Robert E. Barnhill,*An error analysis for numerical multiple integration. I*, Math. Comp.**22**(1968), 98–109. MR**0226852**, 10.1090/S0025-5718-1968-0226852-6**[6]**Stefan Bergman,*The Kernel Function and Conformal Mapping*, Mathematical Surveys, No. 5, American Mathematical Society, New York, N. Y., 1950. MR**0038439****[7]**G. Birkhoff & C. R. deBoor, "Piecewise polynomial interpolation and approximation,"*Approximation of Functions*, edited by H. L. Garabedian, Elsevier, Amsterdam, 1965. MR**32**#6646.**[8]**Philip Davis,*Errors of numerical approximation for analytic functions*, J. Rational Mech. Anal.**2**(1953), 303–313. MR**0054348****[9]**Philip J. Davis,*Errors of numerical approximation for analytic functions*, Survey of numerical analysis, McGraw-Hill, New York, 1962, pp. 468–484. MR**0135721****[10]**Philip J. Davis,*Interpolation and approximation*, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1963. MR**0157156****[11]**Philip J. Davis and Philip Rabinowitz,*Numerical integration*, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1967. MR**0211604****[12]**Michael Golomb and Hans F. Weinberger,*Optimal approximation and error bounds*, On numerical approximation. Proceedings of a Symposium, Madison, April 21–23, 1958, Edited by R. E. Langer. Publication No. 1 of the Mathematics Research Center, U.S. Army, the University of Wisconsin, The University of Wisconsin Press, Madison, Wis., 1959, pp. 117–190. MR**0121970****[13]**M. Golomb,*Lectures on Theory of Approximation*, Argonne National Laboratory, Argonne, Ill., 1962.**[14]**Preston C. Hammer and Arthur H. Stroud,*Numerical evaluation of multiple integrals. II*, Math. Tables Aids Comput.**12**(1958), 272–280. MR**0102176**, 10.1090/S0025-5718-1958-0102176-6**[15]**Don Secrest,*Best approximate integration fuormulas and best error bounds*, Math. Comp.**19**(1965), 79–83. MR**0193752**, 10.1090/S0025-5718-1965-0193752-7**[16]**Don Secrest,*Numerical integration of arbitrarily spaced data and estimation of errors*, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal.**2**(1965), 52–68. MR**0179939****[17]**A. H. Stroud,*Integration formulas and orthogonal polynomials*, SIAM J. Numer. Anal.**4**(1967), 381–389. MR**0228180****[18]**J. L. Synge,*The hypercircle in mathematical physics: a method for the approximate solution of boundary value problems*, Cambridge University Press, New York, 1957. MR**0097605****[19]**R. A. Valentin, "Applications of functional analysis to optimal approximation for analytic functions," Ph. D. Thesis, Division Appl. Math., Brown University, Providence, R. I., 1965.

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DOI:
http://dx.doi.org/10.1090/S0025-5718-1968-0230465-X

Article copyright:
© Copyright 1968
American Mathematical Society