Improving numerical accuracy by iteration; application to computing spherical wave coefficients

It is known that numerical errors can be dramatically reduced by simply iterating the original solution. It is shown that this technique can be applied to reduce quadrature errors when evaluating orthogonality integrals. This technique can be applied to any numerical problem where a residual error can be computed. The author demonstrates its use in an algorithm for computing spherical wave coefficients from orthogonality integrals