Total Positivity of the Spline Collocation Matrix.

Total Positivity of the Spline Collocation Matrix.
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DOI：
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发表时间：
1973-11
期刊：
Heliyon
影响因子：
4
通讯作者：
C. Boor
C. Boor
中科院分区：
综合性期刊4区
文献类型：
--
作者：
C. Boor

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摘要：12010WISCONSIN美国麦迪逊大学数学研究中心，Sde Boor，Carl；MRC-TSR-1396DA-31-124-ARO(D)-462*样条，*矩阵(数学)，插值配点法，样条逼近，样条插值，Spline逼近，Spline内插，给出了关于Spline配置式存在唯一性的Schoenberg-Whitney定理的初等证明。利用Karlin对B-样条型配置矩阵全正性的证明，给出了一些B-样条型系数为零的样条型配置存在唯一的充分必要条件。(作者)
Abstract : 12010WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTERTotal Positivity of the Spline Collocation Matrix.Technical summary rept.,Sde Boor,Carl ;MRC-TSR-1396DA-31-124-ARO(D)-462*Splines, *Matrices(Mathematics), Inequalities, Approximation, Theorems, InterpolationCollocation method, Spline approximation, Spline interpolationAn elementary proof of the Schoenberg-Whitney Theorem concerning the existence and uniqueness of spline collocants is given. Karlin's proof of the total positivity of the collocation matrix involving B-splines is then adapted to give simple necessary and sufficient conditions for the existence and uniqueness of a spline collocant with some B-spline coefficients prescribed to be zero. (Author)