一类重心权Hermite有理插值的二阶导数收敛性

研究了一类特殊情形\left(m=\mathrm{1}\right)的重心权Hermite有理插值，证明了该插值函数的二阶导数r_{\mathrm{1}}^{″}\text{?}\left(x\right)在插值节点和非插值节点处分别以O\left(h^{\mathrm{2}d-\mathrm{1}}\right)和O\left(h^{\mathrm{2}d-\mathrm{3}}\right)的速度收敛于函数f^{″}\text{?}\left(x\right)。数值例子进一步验证了方法的有效性。

Convergence of second derivative of a family of barycentric Hermite rational interpolants

In this paper, we further study a family of barycentric Hermite rational interpolants in a special case m=\mathrm{1} and prove that the second derivatives r_{\mathrm{1}}^{″}\text{?}\left(x\right) of interpolation function converges to corresponding function f^{″}\text{?}\left(x\right) at the rate of O\left(h^{\mathrm{2}d-\mathrm{1}}\right) and O\left(h^{\mathrm{2}d-\mathrm{3}}\right) at interpolation nodes and non-interpolation nodes, respectively. Finally, numerical examples further verify the effectiveness of the method.