On the Power of a Posteriori Error Estimation for Numerical Integration and Function Approximation

ID
TR-90-33
Authors
Feng Gao
Publishing date
November 1990
Abstract
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.