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UBC CS TR-90-33 Summary

On the Power of a Posteriori Error Estimation for Numerical Integration and Function Approximation, November 1990 Feng Gao

We show that using a type of divided-difference test as an a posteriori error criterion, the solutions of a class of simple adaptive algorithms for numerical integration and function approximation such as a piecewise Newton-Cotes rule or a piecewise Lagrange interpolation, are guaranteed to have an approximation-theoretic property of near-optimality. Namely, upon successful termination of the algorithm the solution is guaranteed to be close to the solution given by the spline interpolation method on the same mesh to within any prescribed tolerance.


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