Product integration based on Hermite-Fejér interpolation

摘要

The use of generalized Hermite-Fejér interpolation polynomials for product integration is studied. Algorithms for implementing this method are developed and convergence results are proved. Comparisons are made between this new approach and the classical approach based on Lagrange interpolation polynomials. It turns out that integration rules based on Hermite-Fejér interpolation converge in more cases but, in general, more slowly than those based on Lagrange interpolation, when the latter converge.