On integro quartic spline interpolation
On integro quartic spline interpolation
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DOI：
10.1016/j.cam.2012.05.017
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发表时间：
2012-11
期刊：
影响因子：
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通讯作者：
Feng-Gong Lang;Xiao-Ping Xu
中科院分区：
文献类型：
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作者：
Feng-Gong Lang;Xiao-Ping Xu
本文利用四次B样条构造一个逼近函数，使其与一元实值函数在相同区间上的给定积分值相一致。它被称为积分四次样条插值。我们的插值方法是新的，易于实现。此外，它可以成功地工作，甚至没有任何边界条件。研究了插补误差。证明了该算法在逼近函数值和二阶导数值时的超收敛性（分别为六阶和四阶）。数值算例表明，本文方法是有效的，且积分插值四次样条具有更高的逼近能力。
In this paper, we use quartic B-spline to construct an approximating function to agree with the given integral values of a univariate real-valued function over the same intervals. It is called integro quartic spline interpolation. Our interpolation method is new and easy to implement. Moreover, it can work successfully even without any boundary conditions. The interpolation errors are studied. The super convergence (sixth order and fourth order, respectively) in approximating function values and second-order derivative values at the knots is proved. Numerical examples illustrate that our method is very effective and our integro-interpolating quartic spline has higher approximation ability than others.