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The numerical evaluation of Cauchy principal values of integrals by Romberg integration. (English) Zbl 0265.65016


MSC:

65D30 Numerical integration
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References:

[1] Abramowitz, M., Stegun, I. A.: Handbook of mathematical functions. New York: Dover Publications Inc. 1965 · Zbl 0171.38503
[2] Bulirsch, R.: Bemerkungen zur Romberg-Integration. Numer. Math.6, 6-16 (1964) · Zbl 0118.12303 · doi:10.1007/BF01386048
[3] Davis, P. J., Rabinowitz, P.: Numerical integration. Blaisdell 1967
[4] Fox, L.: Romberg integration for a class of singular integrands. Computer J.10, 87-93 (1967) · Zbl 0158.16001 · doi:10.1093/comjnl/10.1.87
[5] Gragg, W. B.: On extrapolation algorithms for ordinary initial value problems. J. SIAM (Num. Anal.)2, 384-403 (1965) · Zbl 0135.37803
[6] Hunter, D. B.: Some Gauss-type formulae for the evaluation of Cauchy principal values of integrals. Numer. Math.19, 419-424 (1972) · Zbl 0231.65028 · doi:10.1007/BF01404924
[7] Kress, R.: Ein ableitungsfreies Restglied für die trigonometrische Interpolation periodischer analytischer Funktionen. Numer. Math.16, 389-396 (1971) · Zbl 0206.46801 · doi:10.1007/BF02169148
[8] Longman, I. M.: On the numerical evaluation of Cauchy principal values of integrals. MTAC12, 205-207 (1958) · Zbl 0084.11703
[9] Luke, Y. L.: Simple formulas for the evaluation of some higher transcendental functions. J. Math. and Phys.34, 298-307 (1956) · Zbl 0070.12805
[10] Lyness, J. N., Ninham, B. W.: Numerical quadrature and asymptotic expansions. Math. Comp.21, 162-178 (1967) · Zbl 0178.18402 · doi:10.1090/S0025-5718-1967-0225488-X
[11] Navot, I.: An extension of the Euler-Maclaurin summation formula to functions with a branch singularity. J. Math. and Phys.40, 271-276 (1961) · Zbl 0103.28804
[12] Navot, I.: A further extension of the Euler-Maclaurin summation formula. J. Math. and Phys.41, 155-163 (1962) · Zbl 0109.28904
[13] Ninham, B. W., Lyness, J. N.: Further asymptotic expansions for the error functional. Math. Comp.23, 71-83 (1969) · Zbl 0185.41004 · doi:10.1090/S0025-5718-1969-0242351-0
[14] Paget, D. F., Elliott, D.: An algorithm for the numerical evaluation of certain Cauchy principal value integrals. Numer. Math.19, 373-385 (1972) · Zbl 0229.65091 · doi:10.1007/BF01404920
[15] Piessens, R.: Numerical evaluation of Cauchy principal values of integrals. Nordisk Tidskr. Informationsbehandling (BIT)10, 476-480 (1970) · Zbl 0225.65037
[16] Romberg, W.: Vereinfachte numerische Integration, Det. Kong. Norske Videnskabers Forhandlinger28, 30-36 (1955) · Zbl 0065.35901
[17] Rutishauser, H.: Ausdehnung des Rombergschen Prinzips. Numer. Math.5, 48-54 (1963) · Zbl 0111.13001 · doi:10.1007/BF01385877
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