A Bound on the L, -Norm of L -Approximation by Splines in Terms of a Global Mesh Ratio
A Bound on the L, -Norm of L -Approximation by Splines in Terms of a Global Mesh Ratio
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发表时间：
2010
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通讯作者：
C. Boor;C. Boor
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作者：
C. Boor;C. Boor
． 设Lkf表示用n+k阶k的样条对/S Lj的最小二乘逼近，其中结序列t = （t × x）。Douglas， Dupont和Wahlbin结合他们关于伽辽金解微分方程方法的工作，证明了Lk的范数Hi-^ll…作为L«上的映射，可以有如下的界，Halloo o}。使用他们非常好的想法和一些关于s样条的事实，这里显示即使IILfclU«constk(M\k))'/2具有较小的全局网格比AÍJ '，由M<fc):= max （t±k - (,)/<*/+* - tj）。给出了用连续分段多项式逼近l2的网格无关界。
. Let Lkf denote the least-squares approximation to /S Lj by splines of n+k order k with knot sequence t = (t¡)x ■ In connection with their work on Galerkin's method for solving differential equations, Douglas, Dupont and Wahlbin have shown that the norm Hi-^ll,,, of Lk as a map on L«, can be bounded as follows, Halloo o}. Using their very nice idea together with some facts about S-splines, it is shown here that even IILfclU « constk(M\k))'/2 with the smaller global mesh ratio AÍJ ' given by M<fc) := max (t¡+k - (,)/<*/+* - tj). Ui A mesh independent bound for L2-approximation by continuous piecewise polynomials is also given.