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中文摘要：
文章构造了一类具有线性分母的二次Hermite有理插值样条，它在插值区间上C^1连续并且对一次多项式精确成立；讨论了在内节点和半节点二阶导数的跳跃量，得到了被插函数在不同光滑度情况下的跳跃量的估计式，并给出了该样条的一种误差估计以及它在插值区间保持凸性的充分必要条件。
英文摘要：
In this paper a kind of rational quadratic Hermite interpolation spline is derived. This rational spline not only belongs to C^1 in the interpolation interval, but it also has the precision of simple polynomial. Then the jump values of deviation at nodes are discussed, and the error estimation of jump values when the interpolated function has different smoothness is gained. At last the error estimation of the rational quadratic Hermite interpolation spline is given,and the necessary and sufficient condition is derived for the interpolating curves to be convex in the interpolating intervals.
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The dual bases for the Bézier -Said- Wang type generalized Ball polynomial bases and their applicati
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