Abstract
A complete derivation of Romberg integration for an arbitrary sequence of integration steplenghts, using classical interpolation theory only, is given. An explicit expression for the error is derived using Lagrange interpolation. From the general theory developed, several previous known results may be derived as special cases.
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References
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Håvie, T. Romberg integration as a problem in interpolation theory. BIT 17, 418–429 (1977). https://doi.org/10.1007/BF01933451
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DOI: https://doi.org/10.1007/BF01933451