An error analysis for numerical multiple integration. II
Author:
Robert E. Barnhill
Journal:
Math. Comp. 22 (1968), 286292
MSC:
Primary 65.55
MathSciNet review:
0230465
Fulltext PDF Free Access
References 
Similar Articles 
Additional Information
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 [1]
 R. E. Barnhill & J. A. Wixom, "Quadratures with remainders of minimum norm. I," Math. Comp., v. 21, 1967, pp. 6675. MR 0223089 (36:6138)
 [2]
 R. E. Barnhill, "Optimal quadratures in . I," SIAM J. Numer. Anal., v. 4, 1967, pp. 390397.
 [3]
 R. E. Barnhill, "Optimal quadratures in . II," SIAM J. Numer. Anal. (To appear.)
 [4]
 R. E. Barnhill, "Asymptotic properties of minimum norm and optimal quadratures," Numer. Math. (To appear.) MR 0243739 (39:5060)
 [5]
 R. E. Barnhill, "An error analysis for numerical multiple integration. I," Math. Comp., v. 22, 1968, pp. 98109. MR 0226852 (37:2438)
 [6]
 S. Bergman, The Kernel Function and Conformal Mapping, Math. Surveys, No. 5, Amer. Math. Soc., Providence, R. I., 1950. MR 12, 402. MR 0038439 (12:402a)
 [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]
 P. J. Davis, "Errors of numerical approximation for analytic functions," J. Rational Mech. Anal., v. 2, 1953, pp. 303313. MR 14, 907. MR 0054348 (14:907f)
 [9]
 P. J. Davis, "Errors of numerical approximation for analytic functions," Survey of Numerical Analysis, edited by J. Todd, McGrawHill, New York, 1962. MR 24 #B1766. MR 0135721 (24:B1766)
 [10]
 P. J. Davis, Interpolation and Approximation, Blaisdell, New York, 1963. MR 28 #393. MR 0157156 (28:393)
 [11]
 P. J. Davis & P. Rabinowitz, Numerical Integration, Blaisdell, New York, 1967. MR 0211604 (35:2482)
 [12]
 M. Golomb & H. F. Weinberger, "Optimal approximation and error bounds," On Numerical Approximation, edited by R. E. Langer, Univ. of Wisconsin Press, Madison, Wis., 1959. MR 22 #12697. MR 0121970 (22:12697)
 [13]
 M. Golomb, Lectures on Theory of Approximation, Argonne National Laboratory, Argonne, Ill., 1962.
 [14]
 P. C. Hammer & A. H. Stroud, "Numerical evaluation of multiple integrals. II," MTAC, v. 12, 1958, pp. 272280. MR 21 #970. MR 0102176 (21:970)
 [15]
 D. Secrest, "Best approximate integration formulas and best error bounds," Math. Comp., v. 19, 1965, pp. 7983. MR 33 #1967. MR 0193752 (33:1967)
 [16]
 D. Secrest, "Numerical integration of arbitrarily spaced data and estimation of errors," SIAM J. Numer. Anal., v. 2, 1965, pp. 5268. MR 31 #4176. MR 0179939 (31:4176)
 [17]
 A. H. Stroud, "Integration formulas and orthogonal polynomials," SIAM J. Numer. Anal., v. 4, 1967, 381389. MR 0228180 (37:3764)
 [18]
 J. L. Synge, The Hypercircle in Mathematical Physics, Cambridge Univ. Press, New York, 1957. MR 20 #4073. MR 0097605 (20:4073)
 [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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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025571819680230465X
PII:
S 00255718(1968)0230465X
Article copyright:
© Copyright 1968
American Mathematical Society
