Approximation by integro cubic splines
Approximation by integro cubic splines
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DOI：
10.1016/j.amc.2005.07.066
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发表时间：
2006-04
期刊：
影响因子：
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通讯作者：
H. Behforooz
中科院分区：
文献类型：
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作者：
H. Behforooz
几年前，我在牛津大学发表了一篇关于样条函数的论文后，鲍威尔教授批评我们在构造样条函数时，大多数时候使用函数值而不是积分值。他的评论和他的要求成为这项工作的主要动机。本文假定在样条区间[a，B]的每个子区间上，函数y=y（x）的积分值是已知的。通过使用这些值，而不是在节点处的函数值，我们引入了一类新类型的插值三次样条来逼近函数y=y（x）。我们的积分三次样条的结束条件的选择将被讨论。数值例子和计算结果表明，这种近似具有较高的精度.
Years ago, after I presented a paper on spline functions at Oxford University, Professor Powell criticized us for using, most of the time, the function values rather than the integral values on constructing of the spline functions. His comments and his request became the main motivation for this work. In this paper, we assume that, on each subinterval of the spline interval [a,b], the integral value of the function y=y(x) is known. By using these values, rather than the function values at the knots, we introduce a class of new types of interpolatory cubic splines to approximate the function y=y(x). The selection of the end conditions for our integro cubic splines will be discussed. The numerical examples and computational results, illustrate and guarantee a higher accuracy for this approximation.