Monotonicity in Romberg quadrature

Ström, Torsten

doi:10.1090/S0025-5718-1972-0307448-5

Monotonicity in Romberg quadrature
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Math. Comp. 26 (1972), 461-465 Request permission

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.

References

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Absolutely Monotonic Majorants and Their Use for Automatic Strict Error Estimation in Some Areas of Numerical Analysis