Adaptive Integration of Convex Functions of One Real Variable

Abstract

We present an adaptive method of approximate integration of convex (as well as concave) functions based on a certain refinement of the celebrated Hermite–Hadamard inequality. Numerical experiments are performed and the role of harmonic numbers is shown.

Keywords

• adaptive integration
• convex function
• hermite–hadamard inequality
• quadrature
• midpoint rule
• trapezoid rule
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