Spline methods for a Birkhoff interpolation problem.

In this paper, we study two new spline methods for the Birkhoff interpolation problem proposed in Costabile and Longo (Calcolo 47:49-63, ). Our methods are based on cubic spline and quintic spline respectively. The new methods are easy to be implemented. They are effective not only in approximating the original function but also in approximating its derivatives. The respective remainders and error bounds are given. Numerical tests are performed. Numerical results confirm the theoretical analysis and show that our methods are very practical. [ABSTRACT FROM AUTHOR]