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中文摘要：
重心有理插值在整个插值区间上具有足够的光滑性、不存在极点,且具有很高的逼近阶。首先基于给定的权构造的重心有理插值来计算导数的近似值,通过适当选择形状参数,插值函数一阶连续且保单调来构造1/1型有理插值样条,最后分析了误差并给出了数值例子来说明新方法的有效性。
英文摘要：
It is well known that barycentric rational interpolation have sufficiently smooth,no poles and high approximation orders,regardless of the distribution of the points.Firstly,given weights based local barycentric rational interpolants are constructed and the approximate values of derivatives are obtained.Secondly,new rational interpolation spline with linear numerator and linea denominator is presented.The sheme has been used to obtain a C1 curve and at the same times preserves monotonicity.Data dependent shape constraints are derived on two families of parameters to enture preserving the shape of the data while the other two families of parameters are left free for user to control and modify the shape of the given data further in the desired region of curve.Lastly,the error and a numerical example are given to show the effectiveness of the new method.
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