Romberg's method is a numerical analysis technique used to estimate a definite integral by applying Richardson extrapolation repeatedly to the trapezium rule or the rectangle, or midpoint, rule, generating its estimates as a triangular array. It is a Newton-Cotes formula, evaluating the integrand at equally spaced points, and requires the integrand to have continuous derivatives for the best results, though reasonable results can still be obtained when only a few derivatives exist; it is named after Werner Romberg, who published the method in 1955.
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