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Error derivation in Romberg integration. (English) Zbl 0268.65019

MSC:
65D30 Numerical integration
65B05 Extrapolation to the limit, deferred corrections
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References:
[1] J. N. Lyness,An algorithm for Gauss-Romberg integration, BIT 12 (1972), 194–203. · Zbl 0242.65022
[2] T. Håvie,Some algorithms for numerical quadrature using the derivatives of the integrand in the integration interval, BIT 10 (1970), 277–294. · Zbl 0208.41003
[3] W. Tollmien,Über das Restglied der Mittelwertformeln für angenäherte Quadratur, Z. Angew. Math. Mech. 29 (1949), 193–198. · Zbl 0039.12603
[4] C. T. H. Baker and G. S. Hodgson,Asymptotic expansions for integration formulas in one or more dimensions, SIAM J. Num. Anal. 8 (1971), 473–780. · Zbl 0221.65049
[5] V. I. Krylov,Approximate calculation of integrals, Macmillan, New York and London (1962). · Zbl 0111.31801
[6] F. L. Bauer, H. Rutishauser and E. Stiefel,New aspects in numerical quadrature, Proc. Symp. Appl. Math. (AMS, 1963), Vol. 15, 198–218. · Zbl 0133.09201
[7] T. Håvie,Derivation of explicit expressions for the error terms in the ordinary and the modified Romberg algorithms, BIT 9 (1969), 18–29. · Zbl 0179.22003
[8] T. Ström,Strict error bounds in Romberg quadrature, BIT 7 (1967), 314–321. · Zbl 0189.48303
[9] T. Håvie,On a modification of Romberg’s algorithm, BIT 6 (1966), 24–30. · Zbl 0143.38703
[10] T. Håvie,On the practical application of the modified Romberg algorithm, BIT 7 (1967), 103–113. · Zbl 0149.37201
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