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Monotonicity in Romberg quadrature


Author: Torsten Ström
Journal: Math. Comp. 26 (1972), 461-465
MSC: Primary 65D30
DOI: https://doi.org/10.1090/S0025-5718-1972-0307448-5
MathSciNet review: 0307448
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Abstract: Monotonicity of one or more derivatives of the integrand is shown to imply a corresponding property of the approximating Romberg scheme. This is of importance in connection with error estimation by majorants [6]. The monotonicity properties are derived from an elementary study of the kernel functions involved. A possible explanation is given of the monotonicity which frequently occurs in applications where nothing is presupposed about the signs of derivatives of the integrand. Finally, a nonlinear addition to Havie's scheme is suggested.


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DOI: https://doi.org/10.1090/S0025-5718-1972-0307448-5
Keywords: Romberg, quadrature
Article copyright: © Copyright 1972 American Mathematical Society