无限多个基点上的三次样条函数插值 |
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引用本文: | 贾荣庆. 无限多个基点上的三次样条函数插值[J]. 计算数学, 1980, 2(4): 345-349 |
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作者姓名: | 贾荣庆 |
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作者单位: | 浙江大学数学系 |
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摘 要: | Schoenberg曾提出如下的问题: 给定一个严格增加的序列Δ=(x_i)_(-∞)~∞及相应的有界双无限序列(y_i)_(-∞)~∞,是否存在一个有界的三次样条函数s,它以Δ为基点且对所有i,有
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CUBIC SPLINE INTERPOLATION AT A BIINFINITE KNOT SEQUENCE |
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Affiliation: | Jia Rong-qing Zhejiang University |
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Abstract: | Schoenberg once proposed a problem on the existence and uniqueness of bo-unded cubic splines interpolating at a biinfinite knot sequence. Carl de Boor gave a sufficientcondition so that he solved part of the problem. This article made an improvment on Boor'sresult by giving a sufficient and necessary condition. Thus we have completely solved the pro-blem that Schoenberg proposed. |
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