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Numerical Integration of Functionsof Several Variables

Published online by Cambridge University Press:  20 November 2018

G. W. Tyler
G. W. Tyler*
Affiliation:
United States Air Force Washington 25, D.C.
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Methods of mechanical quadrature of functions of more than one variable apparently have received little systematic investigation and the few available results are widely scattered in the literature. In this paper a systematic approach to this problem is given and a number of formulae are derived which may prove to be useful.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 5 , 1953 , pp. 393 - 412
Copyright
Copyright © Canadian Mathematical Society 1953

References

1. Aitken, A. C. and Frewin, G. L., The numerical evaluation of double integrals, Proc. Edinburgh Math. Soc, 42 (1923).Google Scholar
2. Bickley, W. G., Finite difference formulae for the square lattice, Quarterly J. Mech. and Applied Math., 1 (1948).Google Scholar
3. Burnside, W., An approximate quadrature formula, Messenger of Math., 87 (1908).Google Scholar
4. DeLury, D. B., Values and integrals of the orthogonal polynomials up to n = 26 (Toronto, 1950).Google Scholar
5. Frederick Gauss, Carl, Werk, vol. 3 (Göttingen, 1876).Google Scholar
6. Irvin, J. O., On quadrature and cubature, Tracts for Computers, No. 10 (Cambridge, 1923).Google Scholar
7. Woolsey Johnson, W., On Cotesian numbers; their history, computation and values to n = 20, Quarterly J. Math., 46 (1946).Google Scholar
8. LaGrangian interpolation coefficients, Mathematics Tables Project (New York, 1944).Google Scholar
9. Clark Maxwell, J., On approximate multiple integration, Proc. Phil. Soc, 3 (1880).Google Scholar
10. Meyers, Leroy R. and Sard, Arthur, Best approximate integration formulas, J. Math. Phys., 29(1950).Google Scholar
11. Milne, W. E., Numerical calculus (Princeton, 1949).Google Scholar
12. Moors, B. P., Valuers approximative d'une intégrale définie (Paris, 1905).Google Scholar
13. Moors, B. P., Étude sur les formules (spécialement de Gauss) servant à calculer des valeurs approximative d'une intégrale définie, Verh. Akad. Wet. Amsterdam, 11.6 (1913).Google Scholar
14. O'Toole, A. L., On the degree of approximation of certain quadrature formulas, Ann. Math. Stat., 4 (1933).Google Scholar
15. Sadowsky, Michael, A formula for approximate computation of a triple integral, Amer. Math. Monthly, 47 (1940).Google Scholar
16. Szego, Gabor, Orthogonal polynomials (New York, Amer. Math. Soc. Colloquium Publication, vol. 23, 1939).Google Scholar
17. Tchebichef, M. P., Sur les quadratures, J. Math, pures appl., 19 (1874).Google Scholar
18. Whittaker, E. T. and Robinson, G., The calculus of observations (London, 1937).Google Scholar
19. Whittaker, E. T. and Watson, G. N., Modem analysis (Cambridge, 1946).Google Scholar