Construction of Dm-splines in L2(m)(0,1) space by Sobolev method
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摘要
In the present paper, using S.L. Sobolev’s method, interpolation Dm-splines that minimizes the expression ∫01(φ(m)(x))2dx in the L2(m)(0,1) space are constructed. Explicit formulas for the coefficients of the interpolation splines are obtained. The obtained interpolation spline is exact for polynomials of degree m-1. Some numerical experiments are presented. Moreover the connection between the obtained interpolation splines and the optimal quadrature formulas are shown.
论文关键词:Polynomial spline,Hilbert space,The norm minimizing property,S.L. Sobolev’s method,Discrete argument function
论文评审过程:Available online 30 July 2014.
论文官网地址:https://doi.org/10.1016/j.amc.2014.07.033